"If you do NOT use straps, do you place your thumbs over the tops of the poles?"
You seem to have pretty strong hands, so I'd suggest you try cupping the top of the handle in your palm going both up and down. If you plant the poles almost alongside your hips going up, and have the length properly adjusted, you should be able to generate plenty of force to offload some of the effort from your quads onto your triceps, lats, posterior deltoids. It won't replace your quads, obviously, but it will ease their load a bit, which I have found makes a difference over the course of a long day. When cupping, you will be able to control the planting of your poles with your thumbs and ring/pinky fingers. All in all, I have found it to be a lot easier on my forearms and wrists, not to mention eliminating strap chafing on the back of the hand, which is a real PITA in hot weather/dusty conditions. If it doesn't work out, you can always go back to straps, but it might be worth at least a try. If you do end up adopting the technique, it would be useful to attach a retainer cord with a hand loop to each pole. You can make them from 2-4 mil Perlon, Kelty Triptic, or just about any light cordage. Shouldn't weigh more than a few grams each.