Emailing his boss is likely to get you dismissed-
One suggestion/solution may be to simply ask for a 28 day supply- creating a standard every 4 week refill appt - same day of the week on a rotating 4 week time schedule. That would avoid the 30/31 day conflict with monthly fills- you new refill would be every 4th week.
You should have enough meds on a 30 day supply to get you through the end of day 30- then pick up your new prescriptions as soon as the pharmacy is open on the 31st day.
If you were picking up/filling on day 29 before- that left with you with two days of meds from each prescription you filled on day 29- so in your drs mind and by your insurance company’s perspective- you should have a bit of a back up supply on hand- hence only allowing you to pick up new meds on day 31.