Brand new gear supplied by a major rear end company and defective out of the box.
That wouldn't be a first, I assure you!
Don't be turned off on B.W. T10's as they were a good transmission in their time. And, here in the peanut gallery we all await your solution to your endeavor, as none of our knuckles are getting bruised in the process (where that popcorn icon thingy?).
As long as your having fun R & R ing transmissions, and you should be getting proficient at the task (always look at the bright side!) , and since you have the advantage of spares (what luck!), my I suggest taking the side shift side cover assembly from the second unit (that "pops" out of gear) and install on the first that gets stuck in 2nd gear, and test the function. Perhaps at least in this test one could rule out the shift mechanism anyway.
Unfortunately, the solution to the issue will require hands-on observation, and this makes it impossible for the solution to come from a forum, but perhaps some thought may be provided which may spark the investigation and solution, perhaps?
Scott.