A big 30 like an ultra mag, 30-,378, or a 300 Lapua shooting a 140 or 150 is going to put you way above 3300. I guess that will extended your MPBR, but you're going to suffer the typical issues with these setups. One is bullet performance. You'll need to choose a tough bullet to be sure you get good symmetric mushrooming and enough enough bullet shank left to drive straight through the vitals for clean kills at closer ranges. These popular soft LR bullets will give poor results at close ranges and super velocities. Plus inside 500 yards they are uneeded.
A copper bullet of some sort would be where I'd start since you're only going to 500 yards, a partition type like a Swift would be my second choice.
The other issue these setups usually suffer from is finicky accuracy. It can be tough to find a combination to shoot consistently accurate. It can be done but sometimes you gotta roll the reloading dice a bunch, which can burn barrels fast. But, keeping under 500 yards you could suffer 1.5 to 2 MOA accuracy and still work on a lot game shots less than 500.
Depending on atmosphere you're going to be so where in the 20-30in drop range at 500 yards, so due on holds on deer and Antelope with no correction is gonna be iffy. On Elk you could likely get away with some Kentucky windage as they say.
Recoil you said wasn't an issue, plus with a good brake that nullified.
With as easy as it is these days you range and dial elevation correction, I'm just curious why choose such a setup? With a good Rangefinder and good BDC Reticle and proper practice you could have really fast shot setups to 500 yards and shoot something a little slower and a lot more forgiving..
Just saying, but to each their own.
. Good luck