Since Tri-Tip is one of my favorites also, I'm pitching in on all of the slicing comments.
I actually cut mine into two pieces before I start slicing. That cut is generally right off the middle tip, with the grain.
That gives you two smaller pieces that can then be handled easier, and cut against the grain.
I like grampyskids tip of also then slicing on the bias (I'm guessing that means at an angle!). I will definitely try that next time.