I have. The Hornady 110 shoots about 0.75 to 1.0 MOA from my rifle for 5 shots, And the Speer 125TNT has been a favorite for years, to the point that I bought them in the 500 bullet bulk packs. They're great in the Garand (30-06) for local 100 and 200 yard matches. Both offer much less recoil, so your point is well taken.Have you tried lighter weight bullets? With new bullet construction your 125-130gr bullets perform as well as standard cup and core 165gr bullets, and you could load them on the lighter side of the normal range and have a low recoil round that still has a good velocity for an acceptable point-blank range for hunting.
Part of this is just an exercise in seeing if I can make something work. Having shot good groups with the 165SST at greatly reduced loads led to a mention of that 30303 bullet, and got my mind working. Then, actually seeing a box locally, and the chase is on! Using it to take a deer or loading for someone to do that would be a bonus. It gives me a chance to shoot, and have a purpose other than just slinging lead. My dad did take a doe with a 125 TNT in his 30-06, but that wasn't the application for that ammo when I loaded it for him.
Quick tip, the 125 TNT bulk packs are under $100 for 500 right now at Midway. Pretty good deal for a bullet that works so well in so many loadings.