Michael B, Mark Verber, and Randy Martin capture my feelings on this best.
During the day, if you're a strong enough hiker then just take no breaks, keep moving (doesn't necessarily have to be really fast). Long pants, sleeves, sun gloves, headnet kept handy.
Take a decent length lunch break, in part to make up for no breaks along the way. Ideally somewhere windy, or sometimes you find a spot that's just mysteriously low in bugs and/or the bugs aren't too aggressive. Backup plan: put up your tent!
Evening: eat cold meals only, or if you must, be efficient at cooking the meal quickly. Put up the tent, get in the tent, and stay in the tent. Use a pee bottle. If the bugs are bad enough, skip brushing your teeth for this particular night.
This strategy works best for me when hiking solo, or hiking with one or more hiking partners that have a similar approach. In an ad hoc group setting, if you feel inclined or required to stay with the group, you're sort of screwed --- probably need the chemicals.
Look on the bright side: in the comic books whenever someone falls into a vat of nasty chemicals, they always develop super powers, right? !