Using that criteria a .264 will work fine.

95% of the time anyway, the other 5% you get killed.

A 6.5 mm has been used to shoot thousands of moose. I used a 7 mm. They have been used to shoot elk in the USA.

The .318 WR with 250 gr bullets will kill buffalo fine. Have done for again thousands of buffalo.

I'be shot 14 or so water buffalo with a 9.3x74R, none were full sized bulls though, cows and younger animals. A mixture of brain shots, or one to three body shots each.

ONE cape buff with a .375 H&H. Other bovines with a 9.3x74R.

A whole bunch of bovines with a .450. Water buffalo, banteng, scrub bulls. Plus elephant.

So as you say, few people actually have enough experience these days to say from actual use. I must say the 9.3x74R in my limited opinion was not s preferable as my favourite, the .450. Obvious difference of course. Can't say much about use of the .375. One shot into a cape buffalo, it ran stopped after a while appeared to look better, shot it with a FMJ, it zipped right through. It ran and died.

In the future I want to try out my .404 and 10-bore on water buffalo. For fun.