Although the Simms, Pachmayr, Kick Eze etc. pads will reduce "felt " recoil, there isnt one made that going to take the recoil of an 06 down to 243 ish recoil.
One possible cure for you would be to have a muzzle brake installed on your rifle. I guarantee you it will reduce the recoil of the 06 down to a 243 level. If you do go with a brake make absolutely sure you wear hearing protection as it will increase the sound slightly.
It goes without saying that I am a believer that hearing protection and it should be worn when shooting a 22 and up.

But then some here will tell you that if you need a brake on your rifle you need to switch to a lesser cartridge.


If your stock is plastic you might be able to add some lead shot into the butt and that will reduce "felt" recoil but will alter the balance of the rifle.


Just some thoughts.......