Does anyone know any hosts that will let me buy a new domain on one account but get a new account for that domain?

GoDaddy.com will allow you to get a domain for $1.99 with your hosting purchase. That domain wont be for your hosting account.

Also, I think DreamHost will allow you to do this once you purchase hosting with your other domain. Then via the control panel you should be able to comp a domain for a year. I would email sales just to make sure.