Doctors. Grants, loan forgiveness programs, stuff like that should incentivize people to go into medicine. Have to fix the limits on residencies and such too.

You don't even need those things. Without them, medical schools still accept less than half of those who apply. Let's say they increase capacity so that everyone who applies gets in somewhere. The bottleneck would still be, as you point out, the number of residency slots that Medicare is willing to fund.