Axle End Play Even After Trac Lock Rebuild

Before you go pulling your diff apart, do a simple test to see if the clutches are tight enough.

Jack up on side of the rear, and put the car in neutral. See if you can spin the tire by hand. Then repeat the process for the other side.

If you recently rebuilt your T loc as I did, you shouldn't be able to move either tire. If the clutches and steels are holding, then it's a good bet that they are "ordered" properly. It's far from scientific, but I'd do this first before I'd tear into the differential. If one tire turns easily, then maybe you gotta problem there.

A tight clutch set up in the rear will cause a pop ( could be considered a thunk I guess) going around a corner. That would be the clutches on the respective side not wanting to slip as the inside tire turns faster.
With the pin in, you shouldn't be able to move the axle in and out. With a good axle tube bearing at the end of the tube there should also be zero movement in any direction.

But,..
A loud clunk going over a bump is probably not even associated with any part of the rear internally.

Cheap control arms have very rigid bushings in them. Or conversely, a lot of poly replacement bushings are too rigid for street driving. They do not "give" enough when the rear needs to articulate, and they pop, groan, or......Clunk.

This car have subframe connectors?

Have you looked at the floor behind the driver/ passenger side foot wells for cracks, or broken mount points for the control arms?
I'm thinkin that a clunk going around a corner or over a bump could be more likely a torn floor, or mount point popping instead of any axle related stuff..you should probably tear up your carpet, and check.