1969_Mach1

Just put a manual transmission in it.  Most today won't be able to drive it.

I've so far had good luck with MSD 6ALN boxes.  I've never tried the basic 6A or 6AL boxes and I think (but not sure) they are made oversea.  I recently purchased another 6ALN for a new project and it is still made in USA.  Plus they should be installed in an area that gets good air flow for cooling and obviously as far from heat sources as possible.

I'm curious to see if you can get it tuned and running good with the current combination or ultimately a cam change will be needed.
A Holley 700 CFM mechanical secondary carb Holley list 4778-8 runs good on my mild 351W motor.  A 650 CFM Holley mechanical secondary carb, list 4777, is a little more crisp but it seems to pull harder in mid-range with the 700. 

Very sadly, most all of this type of stuff is from oversea.  Of those two, Raybestos is probably the better option.  You can also try NAPA auto parts,  Their brake parts are Raybestos even though they are repackaged for NAPA.
The rotors on my 69 Mach 1 are one piece. Factory front disk brakes.

Yes, you can check the resistance in the magnetic pickup using an ohm meter.  If MSD doesn't list values for the correct range you can search for that information for a Ford magnetic pickup used in Duraspark ignitions during the 1970's.  I think the MSD magnetic pickup is a Ford style.  At least that's what it looks like. 

I think Mach1 Driver is right.  Your options will probably come down to try another pick up coil, if that doesn't fix it, then another ignition box.  If when there is no spark and you immediately do the paperclip test and that triggers the MSD box, I'd suspect the magnetic pick up again.
I've been using the MSD 6ALN with good luck.  It's basically a more robust version of the 6AL.  Performance is the same as a 6A or 6AL, just built more robust for dirt circle track racing.  They're more expensive so wait for a sale if you can.  I recently purchased another one for another project.  At least the 6ALN doesn't have a label anywhere that indicates made in China.

I can say back in 1980 I watched my oldest brother install a 351W in a 1969 Mach 1 with the torque converter attached to the flex plate.  It was an FMX trans as well.  I guess he was careful enough aligning everything and just rotated the crank at the balancer a little to engage the splines.
To answer your question, I don't think that's what happened, but, I since the motor and trans can lean downward when removing the trans, it can be removed with the torque converter attached to the flex plate.
Maybe the shop should try a torque converter from another manufacturer?
Most of us work on our own classic cars.  These day's I think reputable repair shops that can work on older cars are far and few between.

Are your Koni shocks old and worn out?  If not, it seems like a downgrade to KYB Gas-A-Just shocks.  If you have stronger than stock springs, the KYB shocks will make the ride more harsh.

With the original Bendix booster on my 69 Mach 1 the master cylinder can be removed without having to remove the brake booster.  I guess I got lucky.  From what I understand, the clutch rod from the Z-bar to the pedal might interfere with a 9" diameter booster.  I don't know how true that is.  If that rod clears a 9" diameter booster, that would solve some issues with stock clutch linkage and a Borgeson power steering box.

I have done several ,be careful not to go through the roof when removing ,a good port match ,exhaust and intake  and bump removal will increase power ,so will larger valves ,polish the exhaust ports but do not polish the intake port ,just blend it 

Been a while, but I believe the FMX uses both a vacuum modular valve and a rod from the carb linkage to the trans.  I'm don't know much about automatic transmissions.  But, I believe the vacuum modulator valve controls shift points under normal driving.  The other is to force downshifts, increase line pressure, or both (not certain) under hard acceleration from a normal cruise.

Okay, I watched the first 35 seconds of that video, it was too painful.  Ford needs to bring in some more experienced designers.  First, the thing is hideous.  Second, it looks like a copy of a vehicle from another manufacturer.

Most are aware distributors advertised as Ready-To-Run mean they do not need any type of external ignition box or external ignition module.  It doesn't mean the timing curve is optimized for your motor.
An original distributor would be okay for a mild motor.  But, be cautious of a used or rebuilt original distributor.  The bushing and breaker plate usually wear out.  Bushings are replaced on rebuilt distributors but not breaker plates.  It's been a long time since I tinkered with stock ford points distributors, but I remember when the breaker plate wears, as the vacuum advance increases the timing, the dwell reduces.  I've seen breaker plates worn to the point that the dwell reduces so much the motor starts misfiring when the vacuum advance starts increasing the timing.

Okay, I watched the first 35 seconds of that video, it was too painful.  Ford needs to bring in some more experienced designers.  First, the thing is hideous.  Second, it looks like a copy of a vehicle from another manufacturer.

I'm a little confused as to why it was pinging in the first place with either 98 or 95 octane fuel and only 10:1 static compression ratio.  Is the motor running too lean with that 600 cfm holley carb? Or running too hot?

I have also done the UCA drop on my Mach 1.  But not for any type of wandering issues.  The UCA drop is to reduce the camber change as the wheel travels throughout it's up and down travel maintaining more tire contact with the road.  It has nothing to do with wandering issues.  I use the stock tire size on my Mach1, 215-70 14 on the original wheels.  I have never had any type of wandering issues.

The 4R70 is a good trans.  Our old 1996 Mustang GT had.  It went over 300K.  Still worked fine when we got rid of the car.  I serviced it regularly and installed both a shift improver kit and auxiliary cooler when the car was fairly new.  I've installed both Transgo and B&M shift kits or shift improver kits on those transmissions.  In my opinion, the B&M kit has worked better for that particular application.
However, I don't think the 4R70 was ever installed behind a 351W.  To the best of my knowledge Ford always put the larger E4OD behind 351W and larger motors.

Either way is fine.  When I'm not certain if or how much to pump the throttle I will start cranking first.

What type of mufflers are you using?  Chambered mufflers, especially the small two chamber mufflers tend to cause resonating inside the cabin (more interior noise).  Flowmaster's Delta Flow design chambered mufflers are a little better (less interior noise) than the non Delta Flow chambered mufflers with regards to resonating inside the cabin.

Your 600 CFM Holley likely has an electric choke.  They work good, but, one drawback of electric chokes is they cool and reset faster than the engine cools.  After sitting an hour or two the choke might be closed again, then plus some pumping of the throttle causes the engine to flood.  One other possibility is when sitting for an hour or two with a hot engine, the fuel in the carb bowls heats up, percolates and drips into the motor through the circuits inside the carb, thus, flooding the motor.  One of those thick heat insulating gaskets or a phenolic carb spacer will usually stop that from occurring.  The latter situation is more common when aluminum intakes are installed and the heat crossover passage is not blocked.  Another much less common cause of flooding with Holley carbs when the motor sits is leaking metering block gaskets in the carburetor.

Your 600 CFM Holley likely has an electric choke.  They work good, but, one drawback of electric chokes is they cool and reset faster than the engine cools.  After sitting an hour or two the choke might be closed again, then plus some pumping of the throttle causes the engine to flood.  One other possibility is when sitting for an hour or two with a hot engine, the fuel in the carb bowls heats up, percolates and drips into the motor through the circuits inside the carb, thus, flooding the motor.  One of those thick heat insulating gaskets or a phenolic carb spacer will usually stop that from occurring.  The latter situation is more common when aluminum intakes are installed and the heat crossover passage is not blocked.  Another much less common cause of flooding with Holley carbs when the motor sits is leaking metering block gaskets in the carburetor.

You can check ebay for a used one.

After the dash pad, a few more screws and the instrument panel an be removed.  I was able to cut off the end of the inner cable of an old speedo cable, put in a drill, and operate the speedo on the bench.  Maybe you can rig up something in a drill and check the speedo on the bench.  That's how I found out the noise I had was coming from the speedo itself.  If yours seems okay on the bench, then replace the cable while the dash pad is off.
If yours is a factory air conditioned car, proceeding like you are by removing the dash pad is the only way to get to the speedo cable.

Very well be the cable.  But, I have had a worn speedo make a high pitch metallic chirp-chirp-chirp squeaky noise.  

Changing the steering box does not affect or change the steering linkage or suspension geometry.  With that in mind, bump steer will not occur from simply changing the steering box. It's probably either the tires like barnet468 mentioned or your steering box was not centered before installing the pitman arm and/or rag joint/steering column assembly.
After installing my Borgeson steering box, I reset the toe with a tape measure then did a fine centering of the steering wheel with the tie rod adjusting sleeves and it steers just fine.  I didn't increase the caster like is suggested for better steering wheel return to center, but that doesn't bother me.