Thanks for the tip about 220.127.116.118. I found the same version for the 9900 and confirmed that it resolves the issue on that device as well.
Unfortunately it wasn't that straightforward, since there is a bug on the AT&T network with newer versions of 7.1 code where the mic sometimes doesn't work on incoming calls, and calling parties can't hear you.
So the final resolution was to load AT&T's version 18.104.22.1684, then replace the "net_rim_bt_map.cod" file with the one from the 22.214.171.1248 version. After deleting the pairing, pulling the battery, and recreating the pairing, everything is finally working as it should.
Users not on AT&T won't have to endure the extra hackery, and can just load 126.96.36.1998 and call it a day.
Current: '14 550i xDrive
Past: '11 335i xDrive Coupe
Past: '08 335xi Coupe