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@effendude said, the leadsled is part of your problem due to the lack of deflection and damping in the sled. The reaction forces on heavy caliber carry guns can get much higher in that sled than they would when body supported.
I used to design optical systems and spent some time collecting shock and vibe data on small arms in order to have that data for our stress calculations. I found out firsthand that the forces put on the optics could vary wildly on small arms based on body support versus machine supports. I thought it would be good to use a sled to collect that data since the guns looked like a spaghetti mess with all the accelerometers and strain gages tied to them. So, in an effort to make it easier on myself and the other gun handlers while collecting the data, we accidentally noticed how huge a difference there was if the gun was in the sled.
I used to be the Guinea Pig for my more senior friends when it came to doing the boresighting and development work on their big bore safari guns. Those days required an Advil for sure. But the main point is to suggest a highpower shooting coat with the addition of the sweater underneath. Even if you shoot offhand, that coat will take more of the punishment so you can last longer. There is no choice but to practice with the actual clothes you plan to hunt in at some point, but doing work on the gun or loads is a different story.
I am going to add that I ended up spending as much effort on the mounts as we did on the other moving parts within the sight itself. I didn't see that coming, but it was a lesson I have taught since then. If you use light guns with heavy recoil cartridges, make sure your sight bases and rings are steel, and your fasteners are high strength alloys as well. Be sure to use the recommended thread compounds and torque so you don't strip the receiver threads. There is far too much junk floating around in terms of mounting hardware these days. If your receiver threads are still #6, I would consider having them upgraded to #8.