How did you get your chin straps to work with a full face mask? Did you cut slits at the top of it? Then did you put your chin strap on run them through the cuts and then put them through your hat and bump cap?

I think that would work. I put my face mask on first, then the hat with the straps. I I can get the mask on top of my head and covering my face, but it does run into the straps. Cutting slots could work. You could try if you have more masks and don't mind potentially damaging one.