Hmm, hard to say just by looking at an entry hole. You have quite a few species of burrowing rodents out there, from ground squirrels, to voles to moles to shrews to mice to rats, and several species of each. If you can't get a good look at the actual animals, it might help to narrow down by...
Centrarchid, we are birds of a feather. Are you a wildlife biologist?
All mice that come into our house have been deer or white footed, also. It's not exactly rural here, but not quite suburban either. They can be persistent, but there is definitely a seasonal pattern, with noticeable influx...
And from the look of your acreage, I too doubt you have either house mice or Norway rats. Agree that tall vegetation is excellent for cover, and mowing would create more predator problems.
If they are cotton rats and you are in Missouri, then you're near the northern limits of their range, where cotton rat population is subject to extreme fluctuation with weather patterns. So what you're seeing now might have more to do with factors larger than your predator management, and could...