The effect that sweat has appears to depend on the state of the immune system. If the immune system if functioning well, the sweat would contain a good amount of anti-microbial peptides which would actually help control the seborrheic dermatitis.
As for suggestions, please have a look at a post I previously wrote which summarizes all the treatment approaches I have attempted: Overview of Seborrheic Dermatitis Face Treatments
It covers quite a bit and there is lot’s of tips from readers in the comments section as well.
This is what I’ve been doing to manage my SD for the past couple of months:
My Seborrheic Dermatitis Skin Regimen 2.0
Hope that helps and best of luck.
PS. One of the best things that you can do for SD is to stay calm and avoid overthinking things. Reducing stress can significantly improve immune function and may greatly aid in improving SD.