Add fiberglass rolls across joists in attic if joist cavities not completely filled?
Yes, you can do this, but...

Any gaps between the layers effectively negates the benefit of the upper layer. If unconditioned air is allowed to flow between the layers, the upper/outer layer does almost nothing. By putting the layers in contact with one another, the negative effect of small gaps is minimal. 

I'd fill the cavities with R-11 and run R-19 crossways on top of that. Problem solved for minimal extra expense.