Selmer: you have gotten some good advice, especially from Graybeard. I wouldn't get rid of the 06, just pad up or more heavily protect my shoulder when shooting from the bench.
Most of my shooting is from a bench - get the rifle sighted in, then go to standing or kneeling to see if I am still up to the accuracy of the rifle. I use the PAST Magnum recoil Sheild that Graybeard mentioned and it works for me. But, I will also use a shooting jacket with a padded shoulder, and that also helps.
I believe that shooters take their biggest lickin', so to speak, when shooting from a bench and I have seen some folk take the most horrendous positions at the benches that one can imagine and get the stuffing whopped outta them with even some of the lighter calibers.
If you do not notice the recoil when you are in the field (as you may take only 1 or 2 shots), then it may be something you are doing or not doing at the bench. I am fortunate to have a great range to shoot at, but some of the benches seem to be at the wrong height and the seats don't always match up to give me the best shooting position and I have to get everything just right or I get wimped out pretty quickly. Standing or kneeling is OK, but sometimes benching is just painful, even when I am well padded.
I saw one fella shooting a front stuffer that was just killin' him. He had undergone shoulder surgery a few years ago and was usually ok with shooting but this inline muzzle loader was hurting him. And I saw why - he placed the bottom of the shoulder stock (you know, the narrow almost pointed part of the bottom of the stock) right against the point of his shoulder where the nerves pass under the muscle and then complained of both pain and numbness running down his arm - wonder why............
HTH. Mikey.