Your velocity is very low and your using a very small bullet for big game hunting!
Two manuals show 3100 fps as a maximum load for the 243 105 with 24" barrels.
Even then the distance your shooting big game at is too far for your gun.
Get closer to the game and get a bigger rifle.
The 243 is the legal minium in most places and I doubt they considered the hunter using a short barreled rifle with reduced loads.
Use enough gun!
It's not about the bullet at all. Bergers are fine for considered shots from big game rifles within their range.