X3 diffs can work, but they may require some modifications. I'd send you a link if I was on my personal computer. Try google.
There was a member here with a 3.91 in his non-M, so it has been done.
As far as LSD options go, Performance Gearing (
http://www.performancegearing.com) is the least expensive option I've found. Quality is reported to be high, and Jim Blanton is known throughout the community. A Quaife unit is installed into your current diff, so the gearing you have now remains. You won't get any extra mechanical advantage.
I believe you have a 3.46 final drive. I have a full 3.64 unit from a 2.5i with 17k miles that I would let go for cheap. If you're interested, PM me to discuss.