Manual transmission slop?

I’m experiencing some weirdness with my car (2004 Mini Cooper S), what I can best describe as slop or slack in the drivetrain, and I’d really appreciate some help in tracking down where the problem is.

I recently changed my clutch/flywheel, as there was a knocking sound at idle that went away when the clutch was disengaged. This problem went away, but unfortunately the other symptom that I thought might be fixed by changing it did not, which is a noticeable jolt when braking and in gear, happens at about 1500 RPM. My car has a dual-mass flywheel, so I thought this might be the cause, but after replacing the flywheel, the symptom is still there.

After changing the clutch and getting past the break in period, there is now another noticeable issue of drivetrain slop, especially in stop and go traffic. When I let off the gas it feels like the somewhere in the drivetrain there is a lot of play, and the car yo-yos back and forth. It makes a slight gear noise as well when his happens.

Also, when I jack up one side of the car and leave it in gear, I can rotate one wheel back and forth about 2-3 inches while the other wheel is on the ground. I believe my car has an open diff. I’ve owned a few manual transmission cars and realize some play is normal, but this feels excessive.

I’ve posted on Mini forums and researched others experiencing this issue, and the most common suggestion is to replace the motor/transmission mounts. However, I just had those out as I was replacing the clutch and they didn’t seem bad at all, no torn rubber or anything.

The other possible issue I’ve read is the u-joints in the axles could be going, but I’m not sure how to verify that. When I rotate one wheel, it seems like the whole axle is moving all the way to to the transmission.

If it’s something in the transmission, like differential or something else, how would I verify that? Thanks in advance for reading this!