I already got a settlement from my insurance company. I didn't put anything down on the car, since I used the settlement money to pay my high interest credit card debt. I think asking them for the actual cash value of the car would be a fair and reasonable number.
As for Hyundai, your insurer may try to recover all or part of the cost of the claim with the manufacturer. If so the only benefit you would see from a Hyundai pay-out would be to the extent it exceeds what your insurance company paid.
I would get on the CarMax database and find a car close to the one that got torched and use that as a minimum.Sure, you could find it cheaper from a private party, but then you should be asking for the time you spend looking at cars, etc as part of the cost of replacing your car with an "identical" replacement. I bet they won't bat an eye at CarMax pricing.
I think with the manufacturer you would reasonably be compensated for the time you've spent looking for a replacement and dealing with your insurance company. Also consider that your premiums will probably go up (even though it is not your fault), Hyundai should compensate you for that. Don't forget any accessories that you bought for the car, cd's etc. Full tank of gas? It adds up quicker than you realize.
They should pay out at a higher standard than your insurance company.
It'll be interesting to see if Hyundai requires you to remove your videos of the car burning as a condition of settlement (gag order).
The best rule is this is very much a sliding scale so don't underestimate the cost and degree of inconvenience of such an event. If you go overboard, let them tell you that, don't short yourself.
I can't help but think of the irony that you went to an allergist and got to breathe burning plastic/rubber on your way. I hope you haven't had any respiratory effects. Ideally the fumes stayed out of the car during your getting off of the road.