Yes, i've had this problem in winter, but with combination hair ! How could the sebum go to my roots and not my scalp remains a mystery, LOL !
To udnerstand this, you have to realise the dandruffs you see are probably the result of an irritated scalp. I did two things to get rid of this issue :
-first i went back to my old shampoo Node by Bioderma. I mention it but i don't know its availability in the U.S. Whatever the shampoo, take it gentle, and neutral.This will normalize your scalp, and if it's less irritated, it will also produce less sebum.
-the second step was to apply about twice a week two things : pure provitamin B5 (aka panthenol). This favors the hydration of your hair and skin. I applied this first on my scalp. Then i followed with oil, monoï to be precise. It's important to apply the panthenol first as it's not soluble in oil. I bought it at my supplier for homemade cosmetics, as well as the oil. I think you could still benefit from this if you concentrated the oil on your scalp. Then follow by a neutral shampoo.
Another shampoo i suggest is Head&Shoulders, it's quite good and easily found, for a reasonable price. You can also get Neutrogena T Gel, but the scent is not as fancy, and i've had personally less success with it in the past. Rene Furterer also a shampoo for irritated scalp, but my main inconvenient with this one is it only treats what it's made for, you need a second shampoo to wash just your lengths.