Thanks for the advice! I'd like to avoid killing the mice as much as possible, I really wouldnt feel right about it - we're moving soon anyway, and we're trapping some with an old travel cage. There aren't all that many at the moment so hopefully it won't become that much of an issue
I'll keep those in consideration though if there ends up being a lot of them!
I would just keep him in the bin cage for now, but I don't think 80x50's big enough for a Syrian, and his wheel takes up a lot of space (it's a large flying saucer wheel) ^^"