I'm installing a ledgestone back-splash behind my range. I will be applying multiple coats of stone sealer to help protect against grease splatter. Attached is a picture showing the portion of the back-splash I've already installed and the range hood I'll be installing over the range.

The problem I'm having is that the ledgestone has random thicknesses with a tolerance of approximately +/-3/16". When I install the range hood on the ledgestone I want it to sit flush, or at least even on the back-splash.

I would like to install the back-splash before the range hood, in case the hood ever breaks. I do not want to search for a replacement that fits in the exact location. There is also a tempered glass top on the hood, so that would be a nightmare to try to install the back-splash around.

One idea I've considered is attaching strapping to the wall behind the chimney and fan section of the range hood to bump that out 1/2" (approx. thickness of back-splash). Then the range hood would float over the back-splash.

Or I could just install the range hood and then the back-splash around the hood, but like I said above that would be a pain.

Does anyone have any experience doing this or other recommendations for how I should go about installing my back-splash / range hood?

Thanks in advance!