If it makes you feel better, Massachusetts (your totally opposite "sister-state" way to the Northeast) also requires an original, signed bill of sale, too, regardless of a new sale or a used car sale.
Just to add to Alan's comments (all good) - Be prepared with ALL of the documentation you can possibly find to support what you're trying to do, but ONLY give them what they ask for unless it's all going south and you think that additional info will help your cause.
It's also OK to simply say, "I don't think this is working so I'm going home to re-think it," and get up and walk out. They won't really care, trust me - You're just one of dozens they see every day.
Then go to a different DMV office as Alan recommended and try again there - Different DMV people might (probably) understand things totally differently. And don't be afraid to ask for help from their supervisor - Sometimes that can make a big difference. too.
I've also found, here in Massachusetts, that visiting the head office of the DMV has ALWAYS been easier than dealing with a satellite office, but that might not be an option for most of you in bigger states.