For gophers, smaller is better. Well, small cartridge. Big heavy barrel to soak up all that heat and radiate it out at a faster rate. Heat is your enemy in high volume shooting. The 204 would be a superb choice, although it wouldn't be much good past about 3-400 yards in any kind of wind. I've had identical guns in 22-250 and 204 (Remington XR-100's, of you must know). The 204 gets about twice as many shots off between cooling periods as the 22-250, and cools down in the same amount of time once it is hot.
Then again, for 'yotes, a packable gun with more punch may be more desirable. And as shooting is far less fast and furious, heat won't be as much of a concern.
There are some optic snobs out there who look down on Bushnell optics, but the fact is that the 4200 series have outstanding optics. While maybe not as robust as some of the more expensive glass, the clarity is more than sufficient for gopher shooting, and the repeatability and accuracy is fantastic. I like mil-dots for field shooting (as opposed to dialing the range in for each shot)