How about this: You agree to buy breakfast for the staff at a doctor's office/building in exchange for the chance to glad-hand. $50 per meeting means four meetings. You do that enough and you're bound to meet some good people.
Other than that, I'd invest my $200 in my time/travel and attend trade shows, buy business cards, and try to do as much networking as I could with local organizations. Some cost money to join/attend so that would eat your budget but it might lead you to wealthy individuals who like what you're doing. Don't shy away from entrepreneurship organizations either - join the heck out of those since there are tons of ex-doctors as well as friends of doctors.
I don't know - good luck.