Hi banjoguy....if you use tape/s at the nape, try allowing your tape to extend a few millimeters beyond the perimeter of the system so the hair on/ at the edge will stick to the tape...this may help you out and lessen the visual effect of hair standing out from the base.... I too wear similar headgear and am conscious of that effect ... I sit the thing on as loosely as I can usually..
You can do the same thing if using glue....just ` extend` out from the perimeter a small bit and it will at least hold some hair ` flat` in against the skin .......let me know if that works.