Is a permanent profile waiverable for the Green to Gold program?

I mean honestly there is an exception to any policy. Hence the term itself. But the likelihood that it will get approved is extremely low. But to be honest, the worse they can say is no. You should still submit an exception to policy to find out for yourself

I want you deployable if you become an officer.

I’ve probably been a retiree too long to offer any pertinent advice, but... the Army has refs and pubs for every, and I mean everything. Your answer is probably in there somewhere and the ability to take deep dives into regs is one of the skills you’ll need as an officer. Your best COA is to get some informal face-to-face time with an officer or two. I expect you’ll need letters of recommendation from some officers for your application anyway. If you’re in a squared away unit your NCO support channel should be supporting your efforts. Your PL and company XO ought to be your first steps. Find a company grade officer willing to make the time to be your officer mentor. If you can find a mentor that also went Green to Gold even better. They’re easy to spot during Class A inspections. Also remember that there are other pathways to officership as well. Exploit all avenues of approach and engage all targets of opportunity.

In the meantime absorb 22-6. Understand the attributes expected of an officer and make them part of your own personal and professional self improvement campaign. If all else fails: find another doctor. Good luck.