I've been in a similar situation-How much time do you want to spend? A box trap like the Squirrelinator works while you're doing other things. Set one or more near the burrows and bait with something they like. You may have to leave the doors wired open at first to get them used to going in. The trap comes with a tub to dispatch the catch by drowning. I've used and still use these in situations where being next to a road with a gun is a bad idea. A combination of shooting and trapping should be pretty effective.
I cleared our 50 acres in 2010 with a .22 cal Beeman R9 breakbarrel, but I was a lot younger and more patient back then! I would do patrols morning , noon and evening.
A warning-the crack of a headshot is moderately addictive!
I have ground squirrels to thank/blame for my obsession and large collection of airguns.........