Academically, you are probably right, DII is a good fit.
In terms of times, you could be very successful at DIII, I think you would fit in best at DII, but DI is not out of the question.
I suggest the Missouri Valley because I know it is a decent conference with coaches who I feel will develop their athletes, and I think your times could earn you a walk on spot.
Like DIII, there would be no scholarship dollars available most likely. But since cost seems to be important, and you potentially have Med School in your future you should try to keep costs low.
I am from the west, and maybe things are changing, but a few years ago I talked with two residency canidates out of the University of Utah. One did pre med at Idaho State University the other at Harvard. Both had good scores in their undergrad and tested well, and had a relatively easy time getting into the UofU medical program. The difference was the ISU grad (who was an Idaho resident) started med school with no debt, the Harvard grad had about $25K in student loans before med school. Both racked up another $40K doing med school in SLC.
My point is that some mid majors have strong academic programs, admittedly not as strong as some private DIIIs and some big DIs. But if cost, academics, and the ability to compete in college are all important to you a mid major may be the best option. The Missouri Valley is the mid major conference in your area.