transmission / diff issues

[E46m3zcp]

I generally try to post more specific questions, or when I struggle to troubleshoot something but I have done already a good amount of investigation. Disclaimer: This is more of an initial brainstorm.

Starting with the symptoms:
- Aggressive shifting makes a loud thud (SMG in 5th or 6th setting, full throttle, upshift without lifting the foot from gas for example) --> this is the part I'm the most concerned about, as this car would be driven on track next season.
- Diff growls on tight turns (not sure if it's symmetrical or asymmetrical - meaning if it's only when I turn on one particular side or not)
- There is play in the drivetrain: on/off throttle makes a clunk.
- I spun both wheels one by one while the rear end was jacked up with the car in gear, and spinning the right wheel made the diff clunk, but when doing the same with the left wheel the clunking seemed to come from the front (transmission)
- With the driveshaft removed, spinning the guibo / output shaft at the transmission had some play with clunking.
- Currently, my TPMS light keeps coming on red (I did the procedure to re-initialize the system but no luck) --> this may be unrelated, I am monitoring for a slow leak or something.

Additional details:
- It's an 03 E46 M3 Coupe, SMG
- Diff fluid is fresh, Castrol 75W140 with the Ford / Motorcraft friction modifier
- Guibo and CSB look good at inspection
- I recently did the diff input pinion seal and my torquing procedure for the pinion shaft nut was underwhelming (I used a Sharpie to mark it and an impact to torque it back to (what was left of) my marking... I know don't yell at me lol, lesson learned: use something to counter-hold and a proper wrench, and mark with paint markers, not Sharpies)

That said, about the last point, there is no whine... it's just the clunking. So am I right to think I might have had luck and torqued that nut okay-ish?

I'm thinking I might have to replace or rebuild the diff (mainly because of the growl), but I don't like to throw parts at a car without a proper diagnosis. I'm also suspecting something wrong upstream from the diff (transmission or flywheel perhaps?) What could be my course of action? What would you do with this car?

[sapote]

1- Aggressive shifting makes a loud thud (SMG in 5th or 6th setting, full throttle, upshift without lifting the foot from gas for example) --> this is the part I'm the most concerned about, as this car would be driven on track next season.

2- Diff growls on tight turns (not sure if it's symmetrical or asymmetrical - meaning if it's only when I turn on one particular side or not)
3- There is play in the drivetrain: on/off throttle makes a clunk.

4- I spun both wheels one by one while the rear end was jacked up with the car in gear, and spinning the right wheel made the diff clunk, but when doing the same with the left wheel the clunking seemed to come from the front (transmission)
5- With the driveshaft removed, spinning the guibo / output shaft at the transmission had some play with clunking.
6- Currently, my TPMS light keeps coming on red (I did the procedure to re-initialize the system but no luck) --> this may be unrelated, I am monitoring for a slow leak or something.

7- I recently did the diff input pinion seal and my torquing procedure for the pinion shaft nut was underwhelming (I used a Sharpie to mark it and an impact to torque it back to (what was left of) my marking... I know don't yell at me lol, lesson learned: use something to counter-hold and a proper wrench, and mark with paint markers, not Sharpies)
That said, about the last point, there is no whine... it's just the clunking. So am I right to think I might have had luck and torqued that nut okay-ish?

8.I'm thinking I might have to replace or rebuild the diff (mainly because of the growl), but I don't like to throw parts at a car without a proper diagnosis. I'm also suspecting something wrong upstream from the diff (transmission or flywheel perhaps?) What could be my course of action? What would you do with this car?

1.DME stock software should automatically drops the rpm a bit to synchro the gear before shifting to next gear, so I don't think the tranny is to blame. Could be the diff clutch stack see below.

2. It doesn't mater left or right turn; the growl noise is caused by the diff clutch stack slipping which is normal; the noise noise can be different from car to car and condition of the stack. I wouldn't worry about this.
3. If there is no plays in the drive shaft CV or universal joints, then the clunk is from the diff clutch stack slipping characteristic. To solve this clunk, add flat shims to the side-gear to minimize the plays between side-gears and spiders. Don't use Racing-diff spring shim or any spring shim.
4.spin the wheel or rocking the wheel?
5.Again, spinning or rocking? How many degrees is the plays? The tranny output flange does have plays which is normal.
6. what is tpms?
7. If you set the nut to the exact location as before then it's fine.
8. I wouldn't worry about the growl when turning, but the diff clunk can be damaging at high engine load, so shim the side-gear to reduce the plays in the spiders.

[E46m3zcp]

1.DME stock software should automatically drops the rpm a bit to synchro the gear before shifting to next gear, so I don't think the tranny is to blame. Could be the diff clutch stack see below.

2. It doesn't mater left or right turn; the growl noise is caused by the diff clutch stack slipping which is normal; the noise noise can be different from car to car and condition of the stack. I wouldn't worry about this.
3. If there is no plays in the drive shaft CV or universal joints, then the clunk is from the diff clutch stack slipping characteristic. To solve this clunk, add flat shims to the side-gear to minimize the plays between side-gears and spiders. Don't use Racing-diff spring shim or any spring shim.
4.spin the wheel or rocking the wheel?
5.Again, spinning or rocking? How many degrees is the plays? The tranny output flange does have plays which is normal.
6. what is tpms?
7. If you set the nut to the exact location as before then it's fine.
8. I wouldn't worry about the growl when turning, but the diff clunk can be damaging at high engine load, so shim the side-gear to reduce the plays in the spiders.

Thanks for the reply. I meant rocking, not spining. I have not measured it but would say roughly 5 degrees.

TPMS is the tire pressure monitoring, it shows a red light on the dashboard when a tire is detected to be rotating at a different speed than another

[sapote]

5* backlash on the tranny output flange is normal, but there should be zero backlash from the guibo to the diff input flange.
TPMS is not related to the noise / clunk issue.

So I think the main issue you have is the diff clutch stack slip abruptly, causing the spiders to pound on the side-gears (which drive the output flanges) and the clunk. IOW, if the clutches are completely worn smooth, then then no more clunking as it works just like an opened diff (no more LSD). Shim up the side-gear to reduce the plays which reduces the clunk (the plays in the side-gears is normal, but the jerky slip clutch stack causes the hammering effect on the side-gears).