Here is what goes through my mind on "long shots" while hunting big game.
I would not be limited so much by the rifle or cartridge, but by conditions of marksmanship, and presentation of the target in relation to the terrain, two VERY important details almost never discussed on these threads. Shots at a live animal are very different than shots on paper.
One big difference is that with a good hit in the chest, a deer or any other big game animal can run far enough before expiring that tracking is necessary. Is the game in a location where the animals initial location can be clearly marked? Are your observation and tracking skills up to the task of following a deer from a possibly undetermined location to wherever it ended up? With or without a blood trail?
Almost any decent rifle can be shot much more accurately in "range" conditions than field conditions. Field rests just aren't bench rests. Wind is another consideration that is seldom mentioned. At least in the wide open plains wind drift on a bullet can be a very important factor, enough to make a clean miss at ranges over 300 yds to so. Wind also pushes the shooter around.
Just a couple of thoughts that have encouraged me to limit my shots at big game to under 300 yards. My decision to shoot, or not, - mostly isn't about paper ballistics.