If your trans has the large magnet glued in the bottom of the case its unlikely any parts will come out the drain bung. The fact you can move it in /out of reverse NOW suggests that bottom detent and/or spring are not fitted. I suggest that you select reverse gear manually now then also try to select one of the forward gears at the same time to check that the interlock detent is in place.
Also can you now turn the output shaft when you manualy select neutral?
There was someone with a lock-up problem a while back - that turned out to be the wrong blockers[1-2] fitted to the 3-4 synchro hub. An error like that could cause the trans to bind up while in reverse as the top gear synchro ring would be preloaded.
To be certain the trans needs to come down- a good mech can strip/fit brgs,synchros,etc/reassemble one in about three hours, do you have any like that in your area
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Jac Mac