BTW I think I forgot to mention - there is one way to do non-euclidean geometry in a 2D sidescroller without the visibility shadows that I did: if an entire screenful matches on the two ends of the portal, i.e. if overlaps are one screen away from the respective portal from which they are entered, then this can be done by transparently teleporting, as nothing on the screen would change during this.
A game that does this technique is none other than the original Super Mario Bros. in some of the castle levels (those where going a wrong path transparently brings you back to the start of the level). However in there the teleporting was not entirely transparent - they didn't clone some firebars to the destination side of the portal. This would have had an easy fix, of course; however due to how spawning works, it might have been tricky to put the "new" firebars in the same angle as the "old" ones, so this may be why they didn't.