To replace the tapered bearing is more complicated then the deep-grove bearing for the crown gear.
Replace Tapered Bearing:
1. Use a 2-piece puller to pull the tapered bearing off. You could also make a tool to do this.
2. Then use an inner puller to remove the race
3. Clean the housing
4. Then heat the housing up with a heat gun
5. Carefully drive the race into the housing. Make sure it is completely driven in
6. Put the spacer in
7. Heat the bearing with a heat gun and drive it onto the crown gear
Shim the tapered bearing:
1. Install crown gear into housing dry.
2. Use special BMW tools to check the backlash. Backlash should be check at 120 degree intervals around the crown gear. Maybe you can make a special tool?
3. Backlash should be between 0.07mm to 0.16mm (3-6 thousands of an inch)
I suppose you could measure the old race, bearing, and shim and compare it to the new bearing and race and adjust for the shim. But, this alternate method might be risky.
Check the Crown Gear to the Pinion Gear:
1. Clean off the gears
2. Dry them with a rag
3. Use Engineering Blue to check the contact of the gears.
If you did everything correctly, the contact should be correct. Personally, I would check the gear contact before I changed the tapered bearing to compare it to after. And, remember just because the contact is correct, doesn't mean that the tapered bearing is shimmed correctly.
Then shim the deep-grove gearing. Personally, I would replace the crown-gear bearing and the seal. You already have play, so the deep-grove ball bearings have ground down to a smaller size. Failure is not far away. Not Uncommon for them to fail around 40k miles. You are at 84k?