Definitely go with LSD. 3.64 would be my 1st choice. We put one in my son's 535i when we did the swap and in my opinion it's perfect. I have a 3.91 in my 7 and it's a bit too shallow. A 3.73 would be my 2nd choice but they are somewhat scarce.

Give no concern to swapping axle flanges, they pry out with a screwdriver and you'll want to put fresh seals in it anyway, so that's not an issure.

One issue with auto vs manual diff's will be the input flange if it's different than yours, but you can swap that too. Replace the seal if you have to swap input hubs, but don't mess with it if the donor hub is the same.