Ugh. Calc III? Good lord. 😉
Here's my take on that, cuz I knew a kid in the same situation back in undergrad. Instead of Calc III (or in his case Linear Algebra or differential equations or whatever it was) he took the Psych department's statistics class, and learned about statistical analysis of large groups, group comparisons, analysis of variances, t-tests, z-tests, and all that.
IMHO, that stuff is going to be more useful to you as a physician than Calc III. You don't need calculus for medical school; they just need students to understand the basic principles of differentiation and integration, because your body operates on some of those premises. On the other hand, understanding group comparisons is really the basis for most of the clinical medicine research out there. Of course, statistics isn't *hard,* so it's not like you won't be able to pick it up when they cover it in med school. It's probably easier than multivariable calculus, though.
If you WANT to take Calc III, kind of for fun (you're a "math person") or to distinguish yourself from the rest of the pack, go for it. But I wouldn't do it cuz you think it's the only way to fulfill that requirement.
p.s. In my experience, taking difficult science classes at undergrad doesn't really hold you back as much as the premed deans would have you believe. Take what you want, and speak passionately at your interviews about why you made the choices you did, your love of science, and why you wanted to take the hard courses. If you wind up with a 3.2, but a transcript with classes like physical chemistry, protein folding, kinetics, inorganic chemistry, etc, etc--that's impressive to med schools too. A lot of premeds steer away from those classes to keep their GPAs up...
