I know your derms say food intolerance is not a thing, but that's not their line of expertise. When your only tool is a hammer, all you see are nails.
If you want to test your food hypothesis, and don't want to spend a fortune on a food allergist, try a juice fast and and see if that has a positive effect on your skin. You'd be surprised the foods that Chinese medicine prohibits for damp conditions. http://amycdarling.com/pdf/Avoiding_Damp_Accumulation_Through_Food_Choices.pdf
That said, I can't put any oils on my face. Even taking vitamin E orally seems to make me break out. Fish oil REALLY causes breakouts for me, personally. However- have you gotten your vitamin D levels tested? I found that mega dosing D helped me tremendously. (If you're trying to eliminate oils and need moisture- not all of us do- 99% Aloe mixed with DMAE powder is my go-to moisture/serum. I'm also really sensitive to shampoos and conditioners that end up on my jaw line. )