I don't understand how the grass gets through the plastic but you could try. Using flat thin stone as a base and putting your other stone on top staggered over the joints in the bottom layer. Or as I did in some beds is lay flagstone down under the stone 12 x 18 " pieces letting the edge stick out further than the top stone about 4-6" into the lawn a real easy trim job with the moxwe no weed wacking needed. Butt the stone tight underneath and no grass will ever come through. Mowing is a snap!

Maybe it's a creeping type of grass that gets into it. That's what I have and it just spreads on top of the ground and puts roots down as it goes, so nothing I do will stop it, short of a solid wall a foot higher than the lawn. So determine whether yours is coming in from the side or underneath.