I got another idea, that resembles the cosmological concept of a wormhole more closely: do away with the central squares d4, d5, e4 and e5 (the wormhole) altogether, and imagine two such boards glued back to back. Orthogonal slides that hit the wormhole would cotninue back the way they came, but on the other side (e.g. d1-d2-d3-d3'-d2'd1'). Diagonal moves that hit the corner of the wormhole do the same; when they enter the wormhole elsewhere they would 'reflect' from it, but on the other board (e.g. b1-c2-d3-e3'-f2'-g1'). Knights would be imagined to first make an orthogonal step, followed by an outward diagonal one (like in Chinese Chess, but jumping), subject by the same rules for each of those.
I would not combine it with periodic boundary conditions. That just distracts attention from the wormhole.
While considering how to make Infinite Recursion chess better, I had put together the pieces to this new variant. I am in support of both variants being made, but please go check out recursion chess while you're at it. This idea was given to me by an AI (someone also had the idea, but the AI gave it to me first). Simply, this is chess, but the middle of the board (you know, where you put your pawns?), specifically e4-d5 is another chess board you can warp to by moving onto it (you enter the edge specifically). Additionally, you can move from the edge of any board onto another board. Board naming starts from 0 as the origin point, and the number increases the more boards you move out into, and vice versa. All boards contain the starting setup for pieces (excluding the king). Some insparation was taken from 5d chess, as does my next idea, 4d chess (coming soon).