I already adviced 2 option to get this done:
1. Removing the pin that not allows the key to go in with the use of a dremel / drill. Once removed, you'll be able to get the key in.
2. Removing the steering lock housing and unstuck the mechanism that keeps the pin in the tumbler in place, even if you are already set to P.
When going for step one, you still run the risk that the problem is not the tumbler but the lock housing.... after having fixed ours, I would say rarely the problem will be just the tumbler when you don't get the key in.
Removing the whole steering lock housing will be possible even with the car steering locked, so no problem on that. Once you have it out, you should be able to free the "broken" mechanism in the housing, that prevents the pin in the tumbler from retracting.This way you finally can insert the key and rotate the cylinder, so you can get the tumbler replaced.
Let's pretend for a second there is no way you're able to get the key in and rotate it to replace the tumbler. Just replace both at the same time: Lock housing and tumbler. Job done!
https://www.realoem.com/bmw/enUS/sho...diagId=32_1190
Parts involved in your case would be 1 + 6 in the worst case scenario, but as said, you should get away with 1!