A bit like a 270/308. It will do it, but it's on the light end. Be prepared for follow up and use as premium a bullet you can afford, bearing in mind that the bullet is cheap.

A Tsx is a reasonable choice, otherwise I'd use the heaviest you can find. A heavy partition would be another good option.

In general you find that people gravitate towards heavier cartridges once they've followed up and possibly lost one.

I'd suggest the biggest calibre you can shoot well, using a large calibre, heavy bullet at around the same velocities as the 7x57. 9.3x62 is a popular choice, 338 win mag if you feel like it, some prefer a 358 win if a little recoil shy. If you can't shoot it well, it's not going to do anybody any good.

Interestingly fast magnums of smaller calibres (up to 30) are more uncomfortable to shoot in my view than bigger ones. The big ones have more recoil, for sure, but the sharpness of the smaller ones along with the noise makes them harder to manage.