Transmission tailshaft bushings?
 

Since I've been forced into dropping my transmission, this is a perfect time to do other preventative maintenance while the RTV is drying, etc.

An issue I noticed is that the driveshaft has tiny up and down play where it connects to the transmission tailshaft. It's not the U-joints, the movement is in the transmission. Is there a bushing I should replace, or just add a ton of grease when I reinstall it? Or both?

Also going to reinforce my center support bushing with polyurethane.... Might as well before it goes and I already have the stuff lying around.

So you're saying the dust shield is moving independently of the transmission?

Try taking a video if the play if you can. There is no transmission output shaft bearing, off the main gear assembly the transmission output shaft floats through the transmission rear extension and only makes contact on the propeller shaft. The propeller shaft is an internally splined shaft that goes through the rear extension, rides on the rear oil seal, and fits over the splines on the transmission output shaft like a sleeve. If you have any play it's likely a worn out propeller shaft front section, the most common culprit is normally a worn carrier bearing that's allowing for vibration and play.

However a very small amount of play is normal and when it starts to get excessive it usually blows out that rear oil seal.

Good, that's easy to replace in the future should it get worse. I'm not going to worry about it given all the other work I need to do on a concrete floor in 15 degree temperatures.