Omg, I used to have a cat who did the same, additionally, he turned around and since he couldn't see very good, get his nose in there 🤦♂️. Sorry, I don't really have any advice, except maybe change the litterbox filler? Does he try to bury it?
Cat wheel seems like a sound idea for indoor entertainment.
If there are stray cats in the neighbourhood, or other people let their cats wonder outside, your cat might feel like his territory is invaded and needs to go outside - to deter trespassers and mark his territory and whatnot. At least...
If it's a spinal disc issue, x-ray wouldn't show anything (at least to my understanding). Can it possibly be a sprained muscle though? It is possible he jumped and fell from somewhere and you didn't see it.