No issues at all using both W&W and the HGG together, so your choice of when to use one or both.
Best way to clean is immediately after use with the MRB, warm cycle, extra rinse (if available), and HGG towels by themselves. I prefer to use the grey borderless vs. single soft, as you may get some staining on the white.
If your towel becomes saturated, just switch to a new wet towel. You're probably using too much product...I start with the hood, 5-6 sprays, then it should only take a couple sprays or so per panel as you work your way around the car.