"That was how the garden shop suggested it be applied. I guess I'm
trying to
make the dirt as inhospitable to living organisms as possible. Perhaps
something in the dirt as well as on top of the cloth and rocks? "

I think you're making it a lot harder than it has to be. I've used
Triox applied on top of a crushed stone driveway, no cloth. One
application in spring kept just about all the weeds out until at least
fall.