As shown in my picture, the transmission isn't bolted up anymore(not even in the pic) and the clutch is still mounted on the flexplate. So yes, you can remove the tranny without removing the clutch from the flexplate.
The reason you were having a hard time getting the clutch on last time was because, even though they look like it, the bolt holes are
not all on the same axis. 3 of them are, but one is offset a bit differently, so the clutch will only bolt one certain way to the flexplate.