Goucher is the only exception I'm aware of, but I believe their awards are purely nominal, in the ballpark of $500 or so.
The maximum available from Goucher is $4,000, which is still $4,000 more than is available anywhere else. I'm surprised Goucher even has anything available.
Humble Spirit, I'm afraid that postbacs don't get scholarships for a reason. Premed is a hurdle you have to overcome to prove that you can handle med school. Until you've overcome that hurdle, foundations and other scholarship programs won't be willing to take a risk on you. You're even more of a risk if you decide to switch to medicine later in life. Scholarship programs have had to massively tighten their belts since 2008. The odds of receiving outside aid for a postbac are close to zero.
Having to pay for your postbac is also another way to weed out people who are less dedicated. The sad fact is that Stafford and Grad PLUS loans (postbacs are now considered grad students) are readily available to practically everyone, so there is simply no excuse for people to say they can't afford to attend, either.
You're 99% likely more better off if you simply try to apply to a one-year program asap, attend (state) med school asap, and then pay off your school debt asap. That's the fastest way to make the most money and have the lowest debt.
Caveat: all this applies unless you're urban, poor and black and have an outstanding academic record (GPA and school). If that's the case, you might just get lucky, although I wouldn't know where to look.