Med school was a few years ago for my spouse, but I can answer your questions as I managed the finances.

Keep the stock and slowly transfer it into a sheltered Roth IRA $5,500 a year. You won't have to pay tax when you sell it later (though may need to at the time of transfer).

You are going to have to take debt. The question is what you do with it. You can work your ass off, buy appropriate study materials for the Step exams and score well, and graduate AOA. You can then match into very lucrative fields like Derm or Ortho where the $350k starting salary will make the $250k in debt seem manageable (and it really is). This is a great use of debt.

You can also live a great lifestyle, shirk studying, and end-up with $300k in debt and only a scramble prelim spot in family medicine that will lead to a job paying $150k if you are lucky. This is a terrible use of debt (and this is sadly an actual example).

Finally, do not discount your residency location. All residencies/fellowships pay near the same (with a few perks at some locations). I know fellows in NYC literally coming up short $600 a month for their entire training time. Had they been in a different location, they could have been paying off their loans to a small degree, and high quality residencies/fellowships aren't just confined to major cities.

We have only $4,500 in med school debt left with 1.5 years of fellowship remaining. We keep it because we are only paying 0.08% (not 8%, 0.08%, thanks to incentive programs and floating rates). We did this by saving prior to med school, paying down debt based on our earnings from the moment my spouse entered medical school, keeping our lifestyles muted, matching wisely to a great residency program with a low cost of living, and taking advantage of every cost saving program with loans.

My spouse's job was to do her best at medical school. Mine was to pay for it. We succeeded, and I can't wait until that first attending paycheck arrives.