Looking into the transmission from the shifter hole will not tell you anything.
Like what was mentioned, verify there is clearance for all the gears and you are not hitting something somewhere. Another thing, since those are very weak transmissions, you could have a more serious problem. But without tearing it down you may not be able to tell for sure. It may be an easy fix, or it may be more difficult depending.
Do you still have the old trans? If so, try disassembling it; I found a manual online that helped me with mine, and if you are handy you can learn its internals. Then take the new one out and compare, even use the parts out of your old one to fix the new one, or even just swap out the syncros to the old one. I would just not spend ANY money on the BA, been there, done that and it was a complete waste of time and money. I actually spent less putting in an AX15 with complete transfer case than it cost to replace the reverse gear set that went out in mine. The swap was super easy.