I am impatient and not a fan of "you'll hear something in 1 or 2 weeks" so I did some follow up calls today. This information is likely only going to be relevant to folks in the US, but here goes.
So Hyundai "closed" my case on Thursday last week and "sent it" to Sedgwick for the next step of the buyback process. It took some work but I found Sedgwick's number and called them and they did find me in the system but they claimed they don't have all the paperwork yet from Hyundai. She said it takes 7-10 days, and it has only been 5, and 2 of those were the weekend.
So ok, but I did ask some questions and was nice and polite and she was actually pretty helpful. She told me that the calculation for what the car is worth is based on where you live (so I think I'd say this confirms your own specific state lemon law is what is likely to be relevant here) and I told her for me PA and and I asked if she could tell me how the value is calculated. She looked it up and then said exactly what I'd hoped, she basically said what I'd read about PA's lemon law which is .10 cents per mile only up to the first time the problem occurred (I have no idea how to figure out that date and I don't care, because...) but a limit of 10% max of purchase price for the deduction.
I only have 13,000 miles. So the way I see is it my deduction could be as low as $1300 or even less (the whole "date of first problem" part), but at most 10% of my purchase price which would be around $4000. My personal opinion is, if I hadn't spent $4000 on vinyl wrap, a deduction of $4000 would not be bad at all for 2 years of driving the car. She also confirmed b/c I had no trade in and paid cash I
would be refunded taxes in full.
Finally, I asked about the vinyl wrap I put on my car which cost about $4000. She said I would be able to submit paperwork / receipts and request reimbursement but of course she can't say whether it would happen or what my chances are there. (of course I also have a small concern: what if Hyundai says we don't want the car with wrap on it, it needs to be the way we sold it to you.... the problem there is, the place I went to didn't wrap the bumper, they painted it... which, obviously, I was fine with...at the time.... now, though...

)
Final piece of information: Sedgwick puts the paperwork together, calculates the depreciation deduction based on which US state you're in and your mileage... and then sends it BACK to Hyundai and then
Hyundai will email you an actual offer letter with price, which you can accept or reject. If you accept, they then set up an appointment where you will meet with their rep at a dealership to hand over the car (and get paid).
I will continue to post updates as I go through the process.