Great responses everyone (I am the OP)!

I am not averse to doing some work to keeping things up, but I got
really frustrated with dirty rock in the past. Wayne's idea with
herbicide spraying is intriguing. I've also been frustrated with wood
chips for the same reason (and they blow around). And yes, I do use
fabric underneath. In fact, I got some high-quality fabric to put down
under my new stuff from a local landscape supplier.

Thanks for the great ideas.

Kurt