I haven't ever had that type of sebum, I have the other extreme- greaseball, especially when using shampoo. But I have recently had a bit of a dietry makeover about 3 or 4 months ago, and I can't say I noticed a huge difference in my sebum production. I completely get the omega 3/6 ratio thing, and as a result, I eat lots of what I consider to be healthy fats- eggs from free range chickens, meat from pastured animals, evoo, organic butter etc. I also cut out all white sugar and the only grains I have been eating are soaked/fermented oats for porridge. I don't eat any prepackaged anything anymore, so I don't eat additives.
I thought this may have had an effected my hair when I went WO- after a while I wasn't a complete "otter in an oilslick" and I thought the reduced sebum may be partly to diet... but when WO failed miserable (ykwim) and I went back to shampoo, the oilies quickly returned (I'm now oily within 24hours of washing).
To sum up, my change in eating habits was pretty extreme (lots more fat and protein, lots less processed foods and sugar) and I can't say I've noticed a difference in sebum. Sorry- I wish I could be of more help. I hope you find your solution.