You could try the reverse of what happens here - pour earthworm killer all over your land, so there are no worms to attract the moles -( that's a joke). Here, it's the farms round about us that have no earthworms, so the moles all run to us for sanctuary.
Every few years the numbers build back up and we get the mole catcher in again. Ours doesn't cost as much as yours did. We noticed he always left one behind, to make sure there was work for the future
In fact your best plan is to learn how to catch them yourself - it's a skill but shouldn't be too difficult.
I would never use poison on the land. They used to use I think strychnine, but I would hate to contaminate my pastures that way.