Thanks to everybody for the suggestions. I will have to consider my options. Like many of you have said I really need to be careful of my neighbours' pets. One neighbourhood cat likes to hang out in that same flowerbed (possibly with the hope of catching a gopher) so a safe way of getting rid of them is what I'm hoping to do.
So far tonight I did a variation of the CO gas down the holes, and I ripped up a deck board to be able to put one of the ultrasonic devices under the porch. I then softly covered up their holes; enough that they can re-dig them easily and I'll be able to see if they are back.
And on a side note, I was secretly hoping there would be a "Cowperson's dogs" story in here.