Yeah, "what to do now" is the question. So I started a chat with customer care, and they were great - took all the details and escalated it to the regional office and said they would contact my dealer.
For me, I need to separate "what I want" from "what I deserve on principle." I still want an ID.4, but this is might be the only chance to cut-n-run in case this is just a taste of what long-term ownership will be like. Honestly I started to feel a little bad last night and was wondering if I should just go get my ID.4 and drive it while I wait - the dealer never said I could pick it up or couldn't drive it (I'm not really worried about my own safety, but on principle it's not safe to drive). I'm going today to at least take my carseats back.
Maybe with CARE on the case, the dealership has more options to help me out. I'm not interested in leveraging the lemon law in order to stick it to them, or game the tax incentive system. In fact, I'm kind of worried that I could end up losing significant money if I do a buyback then buy a new ID.4, with the NJ point-of-sale incentive, registration fees, and unknowns. Perhaps I'll do a close read of the Warranty.
I think maybe I'll just ask for an ID.4 loaner - at least then I get a month of free mileage. If this were any other product, you would bring it back and they'd just give you a new, working one (maybe VW should look into the strategies of those amazon sellers who know their product will break so they just keep sending free replacements). So to me, the right thing would be for them to say "I'm sorry we can't fix your car, but here's a new one, and here's something for your troubles."
I don't know how this is going to turn out, but I highly recommend chatting with CARE as a starting point. Laws vary by state but it seems they're eager to act even if you haven't started any official process.