Here is a list of all the registered SBIC funds: redacted, I can share a shorter list if helpful of groups I have talked with that would definitely look at $3m+ healthcare services deals

Came here to suggest this. Download the list into Excel, filter for funds actively making new investments, eliminate duplicate firms (i.e. Fund II, III, etc.), then start researching the websites which usually have pretty well articulated investment criteria. I'd personally start with the funds closest to the target's and your location and work your way farther out, but you can go in any order you like. Also try to reach out to an investment professional at each fund that covers your type of deals (the contact listed in the government database may be a CFO/COO/fund admin type).