In applying to graduate programs, what are best practices for proposing research to investigators before and during the application process?
Graduate programs in the United States (since that is all I know) will typically have a letter you write as part of your application. It is there where you identify an area or areas you are interested in working in. My program in particular requested that I speak to this in the written letter AND identify a few professors and areas of research I want to pursue in explicit fields in my application.

Besides doing the above, you have a few options that all center around getting feedback on your proposal, which I cannot stress enough. I've lost count of the number of times I thought I had an excellent proposal or idea, when in actuality it wasn't all that great; however, having a kernel of an idea gives others a starting point to help guide you into a better direction. One option is to discuss this with your supervisor at NIH and see if there is any potential for you to either present work similar to your proposal or attend a conference to network and speak with people that work in this area. Knowing which conferences to attend could be based on your supervisor's opinion or you can find labs or people working in your field and see where they usually publish.