renew driver license in state A using H1B approval from state B

I am living in state A. I got a job from a University at state B. I have received H1B approval notice, but state A DMV wouldn't allow me to renew it and said I have to renew in state B which is 10 hours drive. My A state driver license expires on Monday (12/15/08), I also need to attend my hooding on that day. If I renew it in state B. I need at least two documents to show my residency in state B. I can get rental agreements, but it is impossible for me to get the utilty bill unless I live there for a month. I am really in a deadlock situation.

Any suggestions will be highly appreciated.