I had the same problem. Had an older gentleman (80+) would come with his ATV and trap the gophers. I gave him $2 a gopher and the county gave him $2. He trapped 194 gophers in one season on about 20 acres. I also used a gopher machine to put down poison.
The problem with the poison is that you can only use the gopher machine when there is enough moisture in the soil that the tunnels it makes won't collapse. Then you have to avoid driving on the field for about a month so that you don't collapse the tunnels. This gives the poison time to work. Also, if there are a lot of grubs and live food they may not eat the poison grain this time of year.
I have found the best solution is to get yourself a bunch of traps and start trapping. If you can stay on top of them, you'll get the upper hand.
The first thing you'll want to do is get the existing mounds leveled off so that you can identify where there is new activity. They will mound after it rains. If its really dry, they don't typically mound. Like the gopher getter, I suspect they need moist soil for their new tunnels not to collapse.
I have a friend who has a machine shop. They buy 6 x 8 foot sheets (or thereabouts) of 3/4 to 1 inch thick plate and they flame cut parts out of it. What's left is a big heavy sheet of steel with a lot of openings where the parts were removed. They gave me 2 of these. I use them as drags. You can drag it all over your field and it doesn't damage the grass to the point where it doesn't come back. Mainly, you just need to knock the tops off the mounds. You could probably use an old bed spring with some concrete blocks for weight.
This is the style of trap that I use. I bought about a dozen of them from Menards and carry them in a bucket on my ATV.
Get yourself a rod to use as a probe. Probe the area around the mound until you find their tunnel. Dig down, insert 2 traps so that you have a trap for both directions of their tunnel. I put a small chain on each trap and stake the opposite end of the chain so that they can't make off with the trap.
Take a shovel and dig a small patch of sod and place that sod at ground-level as a cover over the top of the hole you dug. Pile loose dirt over the sod patch to block any light or air from entering around the sod cover.
I buy a bunch of these red flags on the ends of wires that you see used for marking utilities. I stick one of the these flags in the ground to mark the location of my traps.
Wait a couple of days and then check your traps. One gopher can make dozens of mounds. You don't have to kill a lot of them to notice a huge reduction in mounding.
Makes mowing a lot more pleasant, too!
