I like the Cat idea. Maybe you could rent a good one for a few days. LOL
You are right about the grubs. You can kill the grubs overnight if you use a simple pesticide and water the yard gooooood. The water is what activates the pesticide. You can use plan old dish washing detergent and your garden hose to flush any mole crickets or grubs out of the ground.
(only need to test in a small area) It want kill them, but it will make 'em come out of the ground so you can identify what's under there.
As for the mole you probably have several of 'em so don't give up after you catch 1 and don't tell your buddies what their eating for the 4th!!!