I don't think it matters a lot.
Fuel oil will cut grease, gas will cut grease quicker. But fuel oil also offers "some" lubrication at the same time it's diluting the greasy goo substance that you guys have in your BB's.
Marvel Mystery Oil would also cut the goo and give some lubrication at the same time but probably not as fast as fuel oil would do.
"IF" I had a M3W, which everyone knows I don't, and was in this position, I would plan on running the rear tire many miles on jack stands to break down the goo without putting a lot of stress on anything at the same time. I would not use gas, but probably just plain fuel oil to do the diluting until clean. I would imagine this to take several cleanings to accomplish.
If anyone of you has ever drained the rear differential of a standard car, you know that even after tens of thousands of miles the oil is usually still oil, not greasy goo like in the BB's. This tells me that it's not anything in the function of the BB that's creating the goo, it must have started out as goo.
For the life of me though, I cannot imagine anyone ever putting grease in a gearbox like this and expect it to work at the high rpms and load this thing sees. Packing wheel bearings in grease is one thing, but gears at high speed is something entirely different.
Back to flushing out the BB. I see some of you have changed out fluids and then driven a few miles and changed again and just keep repeating this process. I think as JVS has done, he has been able to clean out the goo quite nicely in one major flushing process to a point he's comfortable and filled with heavy duty differential oil and drove the car. I would, as he's probably going to do or already has done, replace the oil one more time within a few hundred miles, but after that it should not be an issue again.
Anything with moly or graphite will turn the grease blacker, but it should not thicken it to goo.
