Your aid package isn't complete because GradPlus isn't in it.
GradPlus: Higher interest rate than private, but unless you have family money you'll just need to suck it up. Grad Plus is a federal program therefore you are in a much larger mass of "customers" with terms that can only be changed by congress. No cosigner required. No limit on how much you can borrow.
Vs. private loans: you have to be the grownup who reads the fine print on what you sign, to understand whether you'll be able to handle repayment during residency during which you'll be making minimum wage. Private loans have none of the acronyms you need to know: IBR, REPAYE, PAYE, PSLF. Private loans are backed by stockholders, not taxpayers, so you have to prove your creditworthiness with a cosigner.
tl;dr: if you have time to study the last ~10 years of whitecoatinvestor.com, then go ahead and investigate paying for med school with a private loan. otherwise stick w/federal.