I finally beat the last sequence of levels :-)
Crossing Over had me stumped for a while, because I was convinced that Nic would eventually build a puzzle around the obscure interaction of pushing monsters with your back. Alas, it wasn't to be.
Congratulations!!! That was an unintended bug that came out of the pushing rules. I don't know of any case where back pushes are useful. I wonder :P
There was a level that got cut that leaned heavily on the monster not jumping into your beam which felt a bit obscure as well.
I think I can see the path through that level, but it looks fiendish and fiddly: probably a good one to have cut!
The only instance in which back pushing would be viable is if it took you all the way to the exit ring, over some combination of switches that otherwise couldn't be simultaneously triggered. But I'm not sure what the process is for actually getting yourself into a back-pushing configuration, as it's one of those things that I discovered accidentally during the long nights of the soul trying to figure out some of the more baroque monster-management levels :-)