You don't get a choice between dealing with the PHP or the board, whatever the board decrees you have to do, and if that includes a PHP than that's it. The best you can hope for is a board attorney who has dealt with the board and PHP, who might have some experience negotiating with them.
It might also help you to contact a psychiatrist that has experience with the board - that can be trickier to find, but the attorneys might know some names. Worth paying cash to see them if you must. Whether or not said psychs are taking new patients or not, when you contact them give them a heads up that you are a resident who is now facing down the med board and PHP and you need help from someone who has some experience treating and representing physicians, and you would appreciate referrals if they can't otherwise help you.
I know residents who got in with psychs whose practices were otherwise closed because of professional courtesy of trying to help one's own. And also got a referral from one psych who had no experience with PHPs to someone who did.
Having your own psych in your corner that has some experience with when physicians get in trouble with the board and PHPs that isn't working for the board or PHP can be extremely helpful in rebutting and potentially changing the hoops the board will require. They can't override the board reqs and the board doesn't have to listen to them at all, but in some cases it can help.