i suggest that you read the links i posted earlier, and also read this link..
https://bicycles.stackexchange.com/q...aper-cartridge
the UN-50 specified by Trek is a compromise unit meant to cut the cost of the bike... and the LENGTH is mostly determined by your frame's design. Emailing Trek may be the only way to know what length they installed in your frame for that particular crankset... Another possible way to find a possible length would be to Look Up the Part Number of the crankset on the bike and hope Shimano has recommended a specific length for a typical MTB.... the kicker being that your 8900 is NOT really a "typical MTB".
there is not much rhyme or reason to the UN designations, other than to identify their Model class.. the usual groupset BB for your XTR parts Was a UN-91, if i recall correctly... the spendy one... there's a NOS one on Ebay right now for $250... and some others too.
And i can't stress this enough.. you might NOT NEED A Bottom Bracket assembly..... those bikes have other "noise" issues described in one of my earlier links.
i'm out..