Ok so I've been playing around with this trying to hit it consistently. The only way I could do that was to alternate between j2 and j3 which is ambiguous enough I guess. The funny this is (as mentioned in the OP) you'll end up on the opposite side no matter what but they'll have to block the j2 as if it weren't a crossup (sort of how DS sword spin can cross you up in the corner but still put you back into the corner). This doesn't work after a f3 however. So here's some ways to get into the 50/50 and how to capitalize on it. Also, empty jumps ftw.
PS: I only tried it on BA, it might be fucked up on Catwoman or something. Will try more some other day.
The J2 mixup does work consistently (i.e- it doesn't keep hitting in the same direction):
-If you hit them with a standing Ice Arrow, e.g- F3 D2 111 xx Standing Arrow (also, it does work after a F3), you can either sky alert or walk back & whiff standing 1. Using these two and varying your J2 timing will ensure it either crosses up/doesn't crossup.
-If you hit them with a crouching Ice Arrow & then Sky Alert, it's generally not a mixup as it usually hits in the same direction. To mix up the J2 after Low Arrow, I found it's best to whiff a standing 1, then J2.
Finally, yeah the swag resets are gimmicks - however they're gimmicks because they always hit crossup. It only whiffs/can be blocked in either direction if you're too slow with the Reload Arrow. Just tested it out on Catwoman to be sure.
I was also testing on my friend and it seems that the J2 generally hits crossup on Lex unless you severely alter the timing of the J2. It's like you just slide over his big, bald head.