That is relatively minor damage that can be fixed at a really good body shop. Why don't you do through your own insurance company to have the damage fixed and have your insurance company deal with Budget? Not sure how Florida insurance works, I only have experience with California.

When my wife's Volvo was totaled while parked, I started out trying to deal with the other guys insurance company. (They had 21st Century, I have State Farm) 21st's "total loss" department gave me a low ball offer and I ended up getting a much better settlement through my insurance company.

State Farm will then send their people to go deal with 21st about the money. This way you don't need to deal with it.

Your body shop should be able to locate parts, that is not that uncommon of a car. They may have to be shipped in from out of state, but they are available.

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84 300DT Puke Yellow. Totalled after 438,000
84 300DT Orient Red. 169,000 (actual mileage may vary)
2002 Explorer EB (wife's)