Myself and one neighbor (among four homes in a 5mi radius) across a highway are the only ones who "maintain" their property. My property is 5ft chainlink fenced and gated. On the outside there are predators, on the inside, our pets, where they are not an easy meal.I'm no expert on moles but we have moles in Texas and I've never seen a concentration any where near dense as what you just described. Are they as thick across several hundred acres or only in your yard? What about other yards? If your yard is the only place so many are found that is a clue. If they are as bad 5 miles in any direction I'd have to ask if their natural predators have been eradicated.
Our Mole problem was a problem when we moved here 25 years ago. The runways and tunnels have our property hollowed out like Swiss Cheese. I've been fighting the GD things by every (except Propane and Dynamite) means I can from a sanity standpoint. Short of renting a commercial Rotovator and going deep, and erecting a 3ft. buried (U.S./Mexico border) steel wall around the whole perimeter, I'm beyond being at wits end.
Eradicate one, it's offspring, siblings and relatives move in.
There are more sink-holes then there is flat sod.