Ok. More on this as I talked with the insurance agent again (who is older than me even and also has experience with a disabled family member so they have a teeny bit more knowledge of what it's like going through this crap).
I asked them to hold off on going after quotes because if something was registered wrong in the past, I don't want it to affect the quotes before I can go through DMV to try to repair this.
They let me know that it was not uncommon in CA to force disabled ppl w vans to