Thanks! The NSTGRO (NSTRF) does not involve a NASA mentor (or a letter of rec from someone at NASA). The application process is similar to most other fellowships. They changed it this year to require the university to submit your proposal if you were already in grad school, which made things a little more difficult, but that just requires some more communication with your PI.
The OSE NASA fellowship does require a letter from a NASA employee, but that one usually doesn't start applications until January.