[mattkrause]

Both of your options already happen.

Basically anyone can apply to the NIH for a grant to run clinical trials. It's not easy: the funding rate for NIH grants in general is in the teens and you'll need to convince the reviews that a) the trial itself generally makes sense and b) you, specifically, can pull it off, but it can be done.

If you find a new use for an existing drug—and run a trial to prove it—the FDA will give you a period of "marketing exclusivity", wherein you will be the only one allowed to market that drug for that condition. It's not quite a patent, but it's meant to be a similar recompense/reward for doing the research.

[entee]

Yes :) I've heard of some of these mechanisms, I think they're a decent balance. All of these issues are fairly complex, it's helpful to have context.