(I know the tranny is in now, but for future reference, perhaps for others)I have no yoke to turn the output shaft. I thought about this a few times because I have spare 904 and 727 yokes but certainly nothing to fit this Tremec.
Loosening the pressure plate sounded like a sure-fire fix but as stated, it just pushed the hydraulic bearing further to the rear when the clutch fingers expanded. That made forward movement of the trans now under spring pressure as well as the interference fit.
I wondered about "Tolerance stackup", a term that I have heard from Mopar Action magazine's Rick Ehrenberg. If the clutch was off center by a couple thousands by one direction and the bearing collar was off in the other direction, maybe the input shaft wasn't aligning properly, I don't know. If the car starts and moves without hard shifting or bearing noises, I'll be dang happy.
Sometimes the splines do not line up perfectly, and once they touch they will stay misaligned since the input shaft spins. (In my experience, this seems more prevalent with 18 spline than 23 spline input shafts.) To avoid that, you can use an output shaft and spin it with the transmission in gear. This will allow the input shaft to spin slightly and engage with the clutch while you are pushing the transmission into place. But if you don't have an output shaft put the tranny in a forward gear and also reverse at the same time. This locks the input shaft. a slight twist of the transmission will do the same thing and allow the splines to align. Of course, you need to immediately "unlock" the transmission to finish installation.