IMHO, I think a .30-06 or a .300 mag of some flavor (I like the .300 H&H) would be a perfect compliment to your .375 H&H and .500 NE battery.

I like the .30 caliber better than something smaller (like a 7mm) as you can use a 200 or 220 gr bullet if you should need to use it on something fairly large like an Eland. (Also, Woodleigh has just come out with a 240 gr .30 caliber bullet.) Plus, the .30 caliber, with lighter bullets, makes an excellent all-around rifle for North American deer hunting, etc.

.30-06, .300 H&H, .300 Win Mag, .300 Weatherby --- pick the one you like best and be happy. My choice would be the .30-06 or .300 H&H. A .300 H&H and a .375 H&H would be a classy pair!

And, there would be absolutely nothing wrong with letting your .338 WM sit between your .30 caliber and your .375 H&H in your battery if you decide to keep your .338 WM. I'm also a big fan of the .338 WM. But, if limited to 3 rifles, then for the light rifle I would pick a .30 caliber to go with your .375 H&H and .500 NE.

My two cents...
-Bob F.