All good points mentioned above.
Not mentioned at all is that felt recoil is subjective to the individual (although personal past experience and flinching due to this past experienced pain or injury was mentioned).
Everyone feels it differently, and just because one is experienced or of larger stature has nothing to do with how they perceive it.
I know a small woman that handles the 375 H&H better than most men.
The LimbSaver recoil pads make a tremendous difference. I use them on all of my harder recoiling firearms and I have gone from 20 rounds of being bruised and sore to 60 rounds and no bruising, soreness or discomfort, even from the bench. The Decelerator work well too, but for the harder recoiling firearms, I recommend the LimbSaver.
Gun fit is going to be as, if not more, important than other factors for some. We are all built differently, and finding a shotgun that fits you, or adjusting the fit if possible, will also help. If you cannot fit the firearm to you, you may need to look at changing the firearm.
A light firearm is a joy to carrying the field all daylong, especially when distances or terrain get long and/or steep or more difficult. It does increase the amount of recoil you will be subjected to. Only you can determine what level of balance will work for you on gun weight and your particular circumstances.
The mention of ear plugs is also a big factor, as the noise makes many "flinch" as much or more than the actual recoil. If plugs do not seem to help, try plugs and muffs...you will usually notice a difference. I use this technique when teaching new shooters and youngsters to shoot. We want the experience to be pleasant so as to increase level of enjoyment and mitigate fear of shooting again.
Shooting position will also effect the perceived recoil...prone and from the bench are worst. Standing is usually best, with proper balance and shooting form, for aiding in reducing felt recoil, as the body can move easier during recoil and make it feel better.
How tight you hold your shotgun to your shoulder, and how rigid your body is can also exacerbate the felt recoil. Be relaxed with a firm, but not hard and rigid grip and body tension, will help. Just keep in mind that you must be able to maintain control during the shot process, and still be able to perform the necessary follow through.
Finding the right balance for you is going to decrease the felt recoil you are experiencing and increase your level of enjoyment and keep you out in the field hunting. Best of luck, I hope you are able to remedy this issue!