Negotiating 1-year delay to my Assistant Professor Offer
Well, as a department head, I would be slightly annoyed that (i) you applied for a position you knew you couldn't take, and (ii) you didn't mention this earlier.

But it is what it is: You have no other option than coming clean, and so being honest should be your first priority. The people you're going to talk to are going to be your future colleagues and you will rely on their good will for the next many years. So playing games is not a useful strategy and all you can do is be forthcoming in explaining your situation, and ask whether there is a way to delay your starting date by one year. There is really no negotiating in this case: You need the department to agree to your demands, because if they don't you have a contract you can't keep (because you can't show up in person) and will likely lose your job. In other words, you're completely at the mercy of the department, and that's how you should treat it: With honesty and humility.