Alright, as an update: I screwed up my attempt at the buffer movement[0], managed to lose pieces from right off my bench[1], then realize that it wasn't going to work anyway as the automatic bridges aren't compatible between the 340 and 343[2]. I nearly pitched it all in the garbage before remember this thread...
[0] : I had it running at 250 degree amplitude, and basically 10 s/d rate, but 9.9ms + beat error. I did a fresh wash then worked on the beat error. I got it to 0.9s beat error after doing the 'look down the posts' trick. I got it together and told myself "you can do a little better...". I did 2 more adjustments (the kind where you have to move the collet), just to find out I messed up the hairspring. Its toast, and my attempts to fix it made everything worse. I then tried my backup hairspring from the other one (the balance staff itself is crusty). It had some gunk on it, so I carefully tried to clean it by dipping in onedip (which I almost never use), and somehow messed up THAT hairspring. Attempts were equally as futile.
[1]: I then decided to just put both movements together without hairsprings to see how it would go, and somehow managed to lose one of the setting lever springs, and have no idea where. THEN, one of the automatic-bridge screws went into space, very first in a while. I suspect I was working too frustrated. This is in addition to a mainspring balance arbor I lost earlier, and a couple of parts that were broken.
[2]: The top plate I have for the 340 auto works and the bottom plate of the 343 auto works have alignment pins going in the opposite direction. So all of this was a failed experiment in the end.
ALL THIS TO SAY: I'm done with this project, and am going to give away the stuff in the below pictures to the first person who will cover shipping (actually, Sheepdoll 1st dibs, since he offered to help ME out, but if he doesn't, OP can have 2nd dibs). I make no guarantees, and in fact, the hands are going to go into the black dial-storage case, instead of the membrain case, since I cant fit it.
I'm not going to spend extra effort beyond a sheet of bubble wrap and some tape on it. However, as it sits now:
1- I have 1 put together with a complete motion works that 'worked' other than the hairspring, which is now toast. Yes, that includes a pallet and bridge.
2- I have the OTHER put together with a complete motion works other than barrel arbor (which is why it is separate), and of course, the hairspring.
3- Dial side: 1 of them is complete other than the hour wheel. The other has nothing dial-side other than the stuff that goes under the setting lever spring/plate. No hour wheel, no minute wheel, no canon pinion. it ALSO has a broken minute wheel pivot on the plate.
4- Case/dial/hands to a 2635-1. No idea if it is a repainted dial, but I thought it was good enough to work on.
5- TWO rotors, but not enough parts to put together a whole automatic works I don't think. Not taking more pictures.
6- I actually bought dial screws, so there are 5 of them in that little packet.
Anyway, the above two have until I go out to lunch tomorrow to take their dibs, else it'll be the 1st person to say 'i'll take it' in my inbox promising shipping costs from US
😀