Excellent write up on your experience. My brother is a 3rd year GS resident, but did a lot of computer programming in medical school using the med records, big data something or another. Did a CS degree in undergrad. Had Google calling on him during 2nd year of MS, but they wanted him to quit med school to come to CA to work full time, he wanted a 1 year internship. No negotiating with the big "G", their way is the only way.
GS Residency programs could have cared less about his patents and stock options in a startup. All they want is to know someone isn't going to quit surgery, and not doing research in surgery was a big minus, though he had other research. It is a brutal residency, and he now doesn't have time to sleep much less pursue his programming. And that he has been out of programming for a few years, he is no longer current, and has moved on to more technical surgical stuff.
Being a polymath sounds good in theory, but in practice, seems like residencies want one-trick ponies, and the trick better be related to the program you are applying for.
Just an n=1, but as I am applying to residency next year, taking this to heart, and I am making myself a one-trick pony, all research and activities related to my app. Narrow, but breadth is not rewarded from what I have seen in family members and friends experiences. I invite others to prove me wrong.