A conventional 264 Win Mag would be better suited to LRH than the 257 Wby Mag. However, that doesn't mean you couldn't build an impressive performer.
While there's clearly a larger selection of 264 bullets available with high BCs from your local retailer, there are (or have been) a few 25 cal bullets with very high BCs.
For example, you might try to reach email@example.com
. He recently indicated that he may start up production of the 25 cal ULD bullets that his predecessor had developed.
I think they had/have 125-156g .257 bullets with BC's ranging from .500-.820 (reportedly).
For such a beast, you would almost certainly need a much faster twist barrel than most all 25 cals. Then, you need the throat done right and you might need to address magazine feeding. But, it would be a really cool sleeper rifle.
Kirby Allen might be the guy to talk to since he's been there, done that, and got the t-shirt. You might just decide to buy one of his rifles.