I'm doubtful of the success you'll have running tapered roller bearings at high speed for very long. I find it strange that you could not find angular contact bearings that were more compact than tapered roller bearings.
Are you running your two bearings back to back, or how far apart are they?
The preload is quite delicate to set for high speed. It should almost be zero.
If we could see a sketch of how you have the bearings laid out, we might be able to give you some ideas. Ideally, you'd have the bearings back to back or something, to prevent having to deal with heat growth of the spindle. Then, at the other end, you'd have a simple ball bearing steady, which is a slide fit in the housing bore. This one would be the one that deals with the heat expansion of the spindle.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)