Free: Contests & Raffles.
I used an 06 for many years and as I grew older the recoil was not fun on the range like you have experienced. Don't notice it in the field though. I switched to a 7mm-08 and that is my go to rifle for deer size animals. Can't tell the difference in killing power. Still have the 06, but it is pretty much a safe queen. I would suggest you try a smaller caliber and see how you like it.
I had recoil issues with my .06 years ago after about 10 shots, though never considered shooting more than a dozen rounds. From personal experience I can reiterate the comments about how swapping in a limbsaver and shooting a lighter round can make a world of difference.
When I am shooting a lot, or have one shot that triggers a nerve in the shoulder, I use a sissy pad. It really helps! https://www.midwayusa.com/product/1002531259?pid=699899