Some times some of the cups will poke up above the frame but thats normal.
What yr are the TT250 clamps?
86-93 uses All Balls # 22-1004 - upper 25-47-15 and lower 30-55-17
So stem same OD, if it was me, id be well on the way to doing the conversion. I cant really help much more without knowing things like stem lengths, frame heights etc.
I am thinking that you may be able to just get the tapered kit for the XT and use the later TT clamps. It may be as simple as that??
Compare the length of bot stems from from the surface the bearing sits on. Are they different?
Is the threaded part for the adjusting nut at the same height?
If the XT taper bearings are not the right stack height, there possibly is other options with the ID and OD you need but different heights. I maybe spacers can be used on the stem before the bearing goes on or a spacer on top of the top bearing/adjuster ring before the top clamp goes on.
Maybe putting the XT stem into the TT clamps is an option that makes it all work?