For starters, you are out at pretty extreme range for .223 anyway. 480 yards, 1/3 mile. Way beyond the 300 yard max for larger targets the military talks about. Most varmints won't keep their heads up for more than two or three shots at that range, so as a practical matter, I don't understand the problem. The barrel will cool while you are waiting for them to stick their heads up again.
If you want more range, I'd suggest a heavier caliber, anyway. At least .308. You are pushing the practical limits of the .223 cartridge at this range. Ambitious, though, I must give you credit.
I had a 24X on my mini, but the scope wouldn't hold zero even in slow fire, so I junked it and went back to iron sights for shots within 300 yards or so. As long as I can consistently hit dinner-plate sized targets in that envelope I'm happy (standing shot, with the forearm braced in the sling for the close stuff, sitting for the far end.)
That was just one example.
Most of the people who benched a Mini and reported their findings found it was incapable of dinner plate groups after the third shot at 100.
If I was hitting the single coyote at 100-150 yards within three shots there wouldn't be a problem.
In the Texas heat, I noticed that once the barrel heated up after those three shots the rifle was useless. A person barely kept them on the paper again at 100 yards. The barrel also didn't cool after that. The 90+ degree heat prevented that.
The design of the Mini is a poor one. The gas system could have been anchored in a reasonable fashion and isn't. The barrels are too poorly made to withstand even a minor heat change. The biggest problem happens when an unknowing owner torques the four gas block screws incorrectly. There have been a lot of Mini's sold after the previous owner didn't understand the proper torque settings. The settings should be finger tight with Lok-Tite.
It's an expensive plinker.