I had a lot of text here but I wrote the tl;dr and realized it said everything the paragraphs did: it's obviously possible to use cardboard for whatever, with relatively minor modifications, so, is there a custom rom or something that allows exactly this? I've dug around a bit and haven't found one.
Also: if you're wondering what this would possibly be useful for, just imagine playing Canabalt or actually basically any other game with VR, without praying that the game devs get on the VR hype train. Immersion is fun.
Also also: I know there are already somewhat similar questions on here, but I think that the answers given previously didn't really answer the question I have here.