Long story short: D tries to extort $20,000 from a victim by telling him there is a hit on the victim's daughter and only he can call it off. They go to the police, police set up a drop in which victim gives D a wad of cash and represents it to be $20k when in fact it is much less. Am I limited to charging this as an attempted F3 theft?

I think you are right on the money. Your facts set forth an attempted third degree felony theft. When all is said and done, it is just a state jail.

We had one like this where a defendant sent some rather revealing photos to an ex-lover and told her he would publish them unless she paid him $10,000. The only thing we could figure was attempted state jail theft...thus only a Class A Misdemeanor.