I never had issues with with porpoising on my F250 extra cab with short short bed while carrying The Arctic Fox 811 (even when everything was stock on the truck). I addressed sag with upper and lower StableLoads. After upgrading to 19.5" wheels, I also added adjustable Rancho shocks to help control the heavier unsprung weight. Between the stock equipment and items added above, I had a great setup with minimal side sway and no noticeable rocking fore or aft.
I did add airbags to haul a heavy trailer this setup (also the reason for 19.5's), but I kept 50 PSI or less in the bags even when loaded at 8000 lbs on the rear axle.
Your porpoising is either caused by soft springs or light shocks. Pretension the springs with StableLoads or add additional spring capacity first. If your suspension still cycles multiple times over bumps, upgrade your shocks to ones with heavier dampening.