Score: Leda 10; gophers 0
I'm hesitant to claim victory in the gopher wars, BUT! Two mornings after I pushed ammonia-soaked Bounce softener sheets down 5 gopher holes, there is no new gopher activity in the backyard!
Keep your fingers crossed! Leda's suggestion just might be working!
P.S. It only makes sense now, but I didn't occur to me that a gopher hole would only head downward for a short while before it turned sideways. So, a flexible stick is helpful when cramming those dryer sheets in there.