I was in a hit and run and don’t have uninsured motorist coverage. My $40,000 car suffered $15,000 worth of damages. It is being fixed in Florida through my Allstate insurance. I am not at fault with my insurance company. I’ve read that it is possible to file a "diminished value claim" against the at-fault party’s insurance or using the uninsured motorist coverage. In this case, neither are available. Is there any way for me to file this claim successfully?

You would have to sue the driver who hit you to recover. Since you apparently don’t know who that is, you are out of luck.