Been thinking about my intended BEC build.
FJR1300 runs "Backward" so a little more thought is called for.
I'm just old enough to have experience with a lot of cars that are no longer common but for which parts are not too hard to find.
Corvair trans is kind of unique in that you can drive it "Correctly" from either end depending on how you do the input shaft.
I used to have a link that explained it well.
As I recall, from the rear the original input passes through the entire diff to the front then to the pinion.
From the front (mid engine) you just use a short coupler instead.
Downside is limited R&P ratio availability, a bit heavy, and U-joint axles as factory.
FIAT trans are pretty light and I expect they are able to handle most bike engines torque.
Fiat made them for normal and reverse rotation engines, so choosing the right unit works mid or rear engine with the diff turning the right direction.
Renault/Lotus trans in 4 and 5 speed variants.
Another light and compact option if you are not running too much torque.
I had a Fuego 5 speed I should have kept, gave it to the guy who bought my Europa, another foolish sale that made sense at the time.
Since these were all used in cars to begin with I think they should work well in light mid or rear engine BEC's.
Some may be able to have unneeded gears removed for further weight savings.
Fiat and Renault also have fairly narrow track if using the original axles.
I know VW bug is the default transaxle and the R&P can be flipped but I am not very fond of them.
Not really pushing these alternatives hard but "In theory it could work".