Brother Tug. I see you joined the forum yesterday. Welcome to AH. It is a good place to discuss such topics with a wide array of people with both technical and hunting/shooting experience. I am guilty of some verbose posts here and elsewhere but do appreciate your discussion. I do not have all the answers but would like to share a few added comments.
I am a life long hunter, and marksman. Qualified NRA Expert at 11yr old, shot on my collegiate rifle team as a young man and am a former USA National Champion rifle marksman, later in life. My first real hunting rifle was a FN FAL black rifle in 7.62x51Nato/308 but at the time I was mostly hunting varmints. A few years later, I put that heavy bitch away and got a nice Mauser custom in 270. Recently, I hunted Africa with a 308 using 180g bonded bullets and a 375HH using Barnes TSX bullets and had stellar performance from both. The little 308 impressed me greatly and took five animals all with one shot kills. But, in my opinion as an engineer your basic premise may be slightly flawed.
For example the first set of the 30-06, 7x57 and 308 lists the 308 as most efficient. If the premise is that this leads to better performance in the field? Then I sincerely and respectfully doubt this. Recoil for example: If I blindfolded you and handed you identical rifles in each caliber and had you fire each one three times all while mixing them up along the way, I would expect that your ability to guess based on recoil and report, which is which would be no better than had you just randomly guessed without firing them. Same for performance on game using the same bullets of same or similar weights. The performance will depend far more on the hunters ability to place the bullets where they need to go than the actual bullet or minor differences in velocity. Just again, my opinion.
Another consideration might be bore wear. The more efficient cartridge might be able to be used longer without burning out the bbl but I would have to examine more data to decide if that theory is correct. This is not much of a factor with a hunting rifle. Last Safari, I took six animals and only fired nine rounds from each of my two rifles and fully half of those in total were shot at the range since one of my scopes got bumped out of alignment by the baggage monkeys. My deer rifle gets fired 3 times before season unless I have changed loads for some reason and then once or twice more at most if I am fortunate enough to harvest a deer or two (I hunt two states). At that rate it can take me four or five years to burn thru a box of 20rds. Most bbls will last a few lifetimes.
Finally, you discussed the 375HH comparing it to a number of other DG options. Comparing the 375 to the 404J, the 416R and others may be a bit of apples to oranges. The 416R is in another class of recoil and penetration than the 375. I would toss in two more the 458WM and the 450NE which are ballistically about identical. All these are considered DG cartridges. And all of them have stood the test of time and are proven on various DG. Excluding use on Elephant which is a specialized trade me thinks, I would posit that since the advent of advanced bullets like the Swift A-Frame, the Woodleigh Hydro and the Barnes TSX, the performance of the 375HH has been elevated somewhat above its original performance with simple soft points and solids. We need to choose our tools for the intended task. If I am hunting Cape Buffalo, it will be with the 375HH. Why? It is fast enough to fully expand a TSX at ranges of 100y or more, (I had one expand to 2x diam on a Wildebeest at 160-180y and over 2.2x at closer distance).
For Buff we limit our shots to 80y more or less. Why? That is close enough to accurately place a good killing 1st shot off sticks and still have time for 2 or more followups should the black bastid choose to charge. Try doing an 80y shot with an iron sighted dbl rifle in 450NE. Or a 458WM. Good Luck. Also, Those cartridges are so slow that out past about 50-80y they will not fully expand a TSX reliably. You can expect about 1.6x at 50y. Assuming the bullets have enough energy to penetrate the vitals at 50y, which is more effective? A .458, 500g slug expanded to 1.6x or 0.732" or a .375, 300g slug expanded to 2.2x or 0.825"? The only real advantage the bigger, heavier bullet has is if you had to shoot the buff in the ass. And even then it is marginal.
I would argue that the 416 Rigby might be significantly more effective despite its lower efficiency but at the price of significantly more recoil than the 375HH or even the 458WM. BTW - data compiled by one of our PH's here on the forum from actual Cape Buffalo hunts over several years show that the 375HH was the most likely to result in a 1 shot kill than ALL the other larger calibers with 80% rate. Why? Not because it is all that much better. But, I would suggest that it was mostly because statistically the hunters are more likely to hit the buff in the right place with the 1st shot using the 375 than the other heavy hitters. For example, I watched a hunter miss a buff at 20y broadside three times with a 600NE. Total miss. He finally hit it in the ass as it ran away resulting in a long stalk to finish it. This was not the cartridge's fault. One shot in the right place with that cannon is almost always going to end the hunt decisively. Keep up the discussion as we all learn from and enjoy these.
Two 375HH TSX slugs recovered from a Wildebeest shot at 160y and 10y. Both expanded well to 2.0x and 2.2x. The long range shot penetrated 36" on a frontal shot. Lodged in the paunch