No suggestions on the adhesive issues, but I recently bought period underwear to try out instead of the disposable pads. I can't give a review yet because I haven't had a chance to actually use them but might be worth looking into! I bought some from Costco but I just grabbed another pair from the grocery store because they were in boy shorts style and I find that more comfortable. Brand that I just bought is Revolcares, Costco one that I bought was Knix.
I usually wear cotton underwear with Kotex pads, biggest issue I've had is sometimes the adhesive pulls on the gusset seam depending on the underwear. I haven't experienced the adhesive balling like that.