Thanks BadAsMo for your description. You've caused me to think through the forces at play when you fire....These are not loaded by pressing forward on the legs - quite the opposite... I pull rearward until I can just feel the tension develop against the rope, then aim and shoot. When I shoot, my shoulder is not into the rifle at all, it's about 1/2 inch behind, but I do cheek firmly taking great care to ensure the rear rest is well behind my check. All recoil is transferred to the ground exactly the same every time.
I pull rearward on the rifle to create tension on the rope to create a slight down force on the rifle. This prevents muzzle jump.
The length of the rope is adjusted to idealize the pivot angle on the bipod legs. If the feet are too far to the rear, the muzzle will climb during recoil. If the feet are too far forward the muzzle will drop under recoil. You can visually see when you have the string length right when the rifle tracks perfectly rearward and the scope reticle stays on target during the full recoil. When you get this right, you will be able to watch your own bullets fly to the target.
What material are you using for the rope?