One of my favorite rifles is a Ruger No. 1 chambered in .45-70; shooting that offhand with suitable loads has taught me that I probably don't want to go to anything more robust (like the .458 Win Mag) with a 7.5 pound rifle. I also have a bench rest rifle chambered in .300 Win Mag. Even with the 8 contour barrel, that can get pretty interesting off the bench.
Your story about the shotgun reminds me that the recoil from a 12 gauge shooting full magnum slugs is something to behold, especially in a 18 inch barreled pump.
The first .458 and .375 I ever fired were the personal rifles and hunting handloads of a respected gunsmith. He was rather large - had an 18" neck! - and had filled the stocks with lead. They balanced and shouldered very well, slowly, but well, and he cautioned me to just let the recoil push me back, and not to fight it. The .458 was loaded with 510 gr. Barnes bullets.
I was amazed at the deep sound, and remarkably softer and slower push of the .458 over the somewhat nastier .375 H&H. Shooting from a bench seems to potentiate felt recoil greatly. One of the most unpleasant firearms I have ever fired was an 18" barreled Winchester 3" 12 ga., off the bench. Bench shooting removes all of the body's recoil absorbing flexibility, and such repeated shots are rare in the hunting fields. It also seems to focus one on the rifle, not so much on delivering a devastating effect upon the "target."
I have since realized that longer barrels are much better choices in all firearms, regardless of cartridge, for power, accuracy and follow-through, and lessened muzzle jump (the most objectional part of recoil), and lessened muzzle flash. The difference can be startling.
Heavier and longer rifles and handguns just work a lot better. Easy carrying is great, but if one's main interest is in hitting the target well, and delivering a telling blow, or several, weight and length is your friend.
I grew up thinking that shorter barrels were a great advantage, and in dry fire, seemed to come up faster, which I took as the key to hitting game, or defending myself. Later on, through using firearms in many different circumstances, it became clear to me that just having the sights pointing at the target was in no way a guarantee of hitting it, or accomplishing the task well, should I hit it. Powder burning/pressure developing barrel length, follow through, stable pointing/aiming, muzzle jump and flash....all adds up to success or failure. Failure can be disappointing, ugly, or dangerous, so facing the truth of what REALLY works is important. Now, I would rather carry more gun, than miss or wound. I would rather have less magazine capacity and a longer gun.
I wonder if one sat lower, making more of a standing type geometry, your .300 would be more pleasant to fire?