Do they make 1/8 inch cement board? If so, were would I find it? I'm trying to fit as thick a piece of wood in a wall as I could for grab bar blocking. I have 1-1/2" of space, then will come the tile. So, in that 1-1/2" I can use 1" plywood + vapor barrier (which I'm counting as zero thickness) + 1/4" cement board + 1/4" morter for the tile, but I think I'd rather reduce the thickness of the morter and cement board and use 1/4" thicker wood. I could plane down a 2x6 so it's 1-1/4" thick or glue 1/4" of plywood to 1" thick plywood, then I'd use 1/8" of mortar and 1/8" of cement board. The cement board would be fully supported by the wood and by plaster or setting type joint compound. It's not like there would be a section of 1/8" thick wall. If it's hard to find 1/8" cement board maybe I'll go with thinner wood and thicker board. I don't really want to make future repairs too difficult.

I've been using 1.5" screws with thread all the way to the head. I now need some 2 inch screws but the ones I have have a smooth shank at the top? Will these work or will they allow the strapping to move in future?