Well, you’re out the $ and the state has it. So not a great chance of getting it back I think. Wish I had better advice.
But in general (and in the future for you) if I don’t like how a DMV office is handling or categorizing something (could be them being wrong, could be me being sneaky) I just leave and try another office if I don’t get the answer I like. Even as a govt agency or private business conducting govt transactions, there are differences in what people understand or do for the customers.
Hell, a few years ago I didn’t want to pay tax on my new to me snow bike and WA title/reg/tax law was fuzzy around snowbikes as they are a motorcycle with an add on kit for the snow and can be turned back into a bike with some work.
I convinced the dmv of a new brand of snow machine which was the brand of the kit and they registered it the way I wanted. First guy to do it. He had to call Olympia and get it put into the system. In front of me.