Driveline thugs when clutch is released

[bazar01]

Car drives smooth no vibration.
But when I shift and release the clutch, there is a thug in the driveline.
I put it on a lift and did some checking.
I checked the guibo and it is good.
Center bearing is good.
It looks like there is a 1/4 inch backlash in the diff input shaft.
I have not checked the u-joints yet.
Is this a differential backlash resetting issue due to wear or just u-joints?
Car has 225k miles.
It still drives very smooth and puts a smile on my face.

I got the car back from my daughter when she got a 2008 Toyota Matrix with manual transmission.

[bazar01]

I think I know where the slack in my diff is. I just found out my diff has an "S" prefix in the diff's tag. When I spun the rear wheel, both wheels turn in the same direction but there was a 1/4' backlash between the wheel rotation and the input shaft pinion rotation.
Is it possible the LSD clutch pack/housing is worn at 225k miles which explains the backlash and the thug in the differential?
I changed the gear oil and it quieted it down a little but there is still a slight thug when shifting and releasing the clutch. I can shift it quietly by rev matching.

Can I have the LSD rebuilt and by who?
Thanks.

[bazar01]

Just wanted to update on this issue.

When I replaced the engine when I got the car, I did not put a pre-load on the drive shaft center bearing.
I read on the shop manual that reinstalling the drive shaft back, to push the center bearing forward by about 1/4 inch to preload the center bearing.
What I did was raise the car, unbolt the aluminum exhaust heat shield and moved the shield forward to gain access to the center bearing mounting bolts, loosen the mounting bolts and pushed the center bearing forward by 1/4 inch.
No more thug or clunk after shifting and clutch released.