If you are new to big bores limit the amount of shooting from a bench. Shoot them first just off-hand at simple targets even if not sighted in.

Use some padding when sighting in or building up handloads.

If you need to, try sighting them in standing up with a rest, rather than shooting from a bench or hunched over. Your body will have more whip and flexibility standing up.

One way to reduce the perceived recoil of your rifles is to have a go at shooting something larger before shooting your own rifles. The 9.3mm will feel soft after you shoot the .375 for example. I think you will find the 9.3 double quite comfortable in comparison depending on how light or heavy the double is. If you have a mate with a .458 or similar see if he can bring that out, only fire a shot or two.

When I started shooting a .375 I found the recoil quite hard especially if shooting around 20 rounds at a time. After getting used to a .450 it feels soft. The 9.3 feels very light now.

Take along your medium calibre rifle and shoot that in between the bigger bores. If you think you might start developing a flinch, give up for the day, or take a rest from shooting them.

When you use them on game you probably won't even notice the recoil . So in my opinion, within limits, recoil is more in the mind than the body. However having said that, if you shoot a number of shots from a big bore, your body will feel the effects afterwards.

If you feel the recoil is getting to you, try making up some lower powered loads eg for your .375. Get comfortable with shooting the rifle.

A good recoil pad is important.

I don't like porting and especially don't like muzzle brakes as I value my hearing more than the alternative.

Don't know anything about internal recoil reducers.