Baits are not always effective if there is plenty of other food for the gophers. Gas cartridges may not be successful, especially in dry, cracked clay soils or sandy soils which let the gases escape from the tunnels. They can tunnel quite deeply, so buried fencing is of very little use. It may interfere with their invasion enough to give you time to use other control measures before they can do too much damage, but it will not stop the gophers. Moving, as you suggested, may be only a temporary solution.
Gophers are problems all over New Mexico and some other states also have problems with moles.
As we develop our beautiful home landscapes, we create an environment which invites the gophers to come visit us.