Ok, here's my problem:

When accelerating, I get a sharp 'bang' each time the transmission shifts, unless I accelerate very slow/carefully...

I have been told by a local shop that the transmission mounts are broken, and this is the cause... Others have said it's a differential problem...

So:

1) How much of a pain is it to change tranny mounts? I have access to a transmission jack & the 'right' tools....

Can I just support the transmission on a jack and swap the mounts out, or is it much more involved?

2) What is the chance that this is NOT the problem, or that the mount failure was caused by something else that IS the problem...

(P.S. I don't race this car, the 'hardest' I drive is stepping on it to merge faster on the freeway)

 

There is only one transmission mount, under the tailshaft housing, supported by the tranny cross-member. You support the tranny (floor jack and a piece of wood works well), unbolt the crossmember and the mount, install a new mount and reinstall the cross-member. Very simple. Should not take more than 30 minutes. Consider using a new mount that is stronger than stock. The Energy Suspension polyurethane mounts are indestructible, but may transmit more driveline vibration to the interior.

I'll move this to the "Drivetrain" forum, since it isn't really "engine" tech.

 

That sounds to me like a broken tranny mount, it's remotely possible you have a broken motor mount, or both. If when it shifts you feel like a thud almost under your seat that's going to be your transmission hitting the floor tho..

Usually when one of the mounts go out they take another mount with them due to added stress. I actually broke, count them.. 6 transmission mounts, just the regular OE mount from GM.. After that I switched to all Energy Suspension poly mounts and man do they make a world of difference, I've never broken a single one and they have a solid warranty backing them. Although I do notice a very small amount of added vibration due to it being polyurethane vs. rubber, but if you didn't know what it felt like before you wouldn't notice it at all.

Change out the trans mount is super easy and if you block the wheels, put it up on jack stands, use a floor jack and a 2x4 and lift the trans just a tiny bit, take the bolts out and swap it.. Just remember to torque them back in..

Motor mounts.. hah good luck with that

 

Yeah man 97 Z28 here with 10 inchers on the rear, you can call me mr trans mount lol, they break like there going out of style, they are very easy to change if you mechanical, but thats been stated above no need to get into that but man a little vibration?? those poly mounts are terrible man, I tried one before and didnt like it but i just got my tranny rebuilt and the guy said try this one from summit, its better but man when your getting on it it feels like a tank, but it wont break....lol. There's no happy medium. If you beat the **** out of car almost daily (who would do a thing like that) then you may want to consider it, but if you only do burnouts or power breaks on rare occasions then stick with the stock. Good luck man.