You would probably have to simply call and find out if you can switch doctors. I know the frustration that can happen with dermatologists. One time my dermatologist tried prescribing me 10% BP. Yeah, that would have murdered my skin, and you can buy it over the counter, so what is the damn point of me going to the doctor if THAT is what I'm gonna get? I knew this for a fact, and I didn't go to school for 10 years to be a derm. I'm with you on the diet thing. It's all BS and a waste of time to try and change your diet.
For what it's worth, I can tell you what has been working for me...
Morning: Wash with Cerave hydrating cleaner, apply Clyndamycin Gel all over.
Night: Wash with Cerave Hydrating cleanser, apply Atralin gel (.05% tretinoin)
I also take minocycline, but you said Doxycycline didn't work for you, and I think they are similar.
This regimen has done wonders, I believe specifically because of the Atralin Gel. It doesn't dry out my skin at all, yet it delivers a pretty potent concentration of tretinoin. I don't even need a moisturizer. It's like the perfect formulation of tretinoin. Ask your doctor about it. As far as I'm concerned, it's the best topical I have ever used, and will never go off of it. EVER.