Not a bad idea at all.  Hope you'll post more info on where you got this garment.  If you are wearing enough DEET that it's actually making you sick - that's not a good sign.  I also use 100% DEET (aka Jungle Juice), but I don't put the stuff on my skin.  I rub it on the cuffs of my shirt and pants, around the neckline of my shirt, and on the brim of my cap.  Still seems to work OK.
Pete2