No response to the question if the bellhousing is original. Misaligned bellhousing equals popping out of gear and gear grinding.

Forget the pedal free play and do like the FSM says, set the play at the throwout fork at 5/32".

Awesome looking Swinger, my buddy has almost the twin to yours, his has a black interior!!!
I'm having similar problems with my 67 hemi GTX, starting to break it down to being the pilot bearing being too tight and turning the trans even when the clutch is depressed, I have had my buddy with the Swinger go through the trans it and it seems that it's real good for a while and than it starts doing the same as what you car is doing, being a nice guy that I am I believe putting some grease on the pilot shaft is creating some of this problem after a while as well as not pre reaming out the pilot bearing, what I have been reading ppl say to not put any grease on the pilot bearing at all, I have used just a dab of lithium grease, my next step is to use a bearing that goes into the A/T torque converter hub area in the rear of the crank, this should be the part number, # BRG FC69907, hope to try this in the next few months.
Good luck to you,

Alot of good replies but none of them garantee you input shaft/disc is free.
With the car running, press the clutch pedal. After 5 seconds try to engage reverse. If the clutch was disengaged it will eventually stop spinning allowing you to engage reverse.

Although my feeling is the problem is in the transmission. If you do not disengage the clutch and try to shift. The gear should not be allowed to go in. Similar to shifting without a clutch. It either goes in when the speeds are matched or it's not going in, but there is no grind.

Yup Dial the bell 1st thing. Its a PITA but Ya gotta start There. All the big trans vendors wont Warranty if out by IIRC 0.003.

Once you get it measured, then get the ROBBMC dowels that will get you realigned. I tried all of the others, its the only one that works.

after clutch work and bell alignment, i use alignment pins to help guide and support the trans when reinstalling it. they can be made by getting some bolts a couple inches longer than those used to secure the transmission. cut the heads off and grind or file a screwdriver notch in the end. using these keeps the weight off the clutch disc when installing the transmission, preventing the clutch disc from moving off center as well as preventing things such as the throw out fork from getting "tweeked". when trans is seated, remove alignment pins and install proper bolts. i use this tip on automatic transmissions as well.

You mentioned changing out the syncros, how were the dog teeth (clutching teeth) on the gears themselves? Were they redressed? Just because you changed the synrcos, doesn't mean the trans is rebuilt. I am assuming the people you had look at it knew what they were doing. If you do end up taking the trans out, pop the side cover and put up some pics. Worn dog teeth will do what you are describing as well. If the trans is a 1969 it will have the ball and detente cover so be careful not to push the shifter levers out or else you will pop out the balls and spring.

The NP833 trannys from 1964 to mid 1971 all had that side cover There are three different synchro assemblys also so they need to match the gears and hubs in the tranny

I'm a newbie on this but I cant help wondering if there is any way to pin it down to either the clutch or the trans before having to take off the bell to check runout there? But that IS what we have been trying to do here all along. keep us updated

you could check the disk gap, throw out bearing clearance and see if the input shaft is tight in the pilot bushing before you pull the trans.

Once apart you can check the pressure plate for broken parts, a bent disk and see the flywheel for a weird wear pattern

I would open the trans last

It's clutch related, and he hasn't answered the question of the originality of the block and the bellhousing .

Chrysler did the final machining of the crank main line, and the pilot hole of the bellhousing, with the bellhousing bolted to the block. The assembly stayed together from that point on. That is why there is a big cover plate on the bottom of the bellhousing, so it could be assembled with the bellhousing in place.

Most people have bellhousing that were not original to the block in the car as most cars are not matching numbers, so there is a runout issue that many do not realize they have.