Dave,
As Flytyer says, learn to use your rifle. A fast flatter bullet doesn't make up for deficiencies in "accuracy", it just/still damages more meat if too much "shock".
A heavier, slower, "loopier" bullet will do less damage, you just have to know where to aim. It's still called accuracy.
A .243 , that you already have, is good.
If you have plans to do "more or bigger" here in the UK or abroad and can really only "service cost" of one rifle then by all means consider a slightly larger calibre.
Same caveat applies, learn to use it. Practice, practice, practice.....
Stan
P.S. 7 x 64 has only ever been a hunting calibre. No problems with "Johnny Foreigner" and should be as acceptable to a FEO as a .308.
Never found a "reasonably" stocked shop in Africa without them 8)
I went Swedish with my UK rifle and then went for a Mauser M03 (9.3 x 62 for Africa) for a heavy calibre. Decided I wanted less than 9.3 x 62 for lighter foreign antelope and was going to go for 7 x 64 having used, and loved it.
Decided to only master one light calibre, not two. Got a second Swede for the Mauser and am working on maximising what I can get out of "same calibre, two rifles"