The Pelican equivalent for Tile is
John Bridge. I believe they have a calculator for determining if your existing flooring/joists are up to the job.
Also if it were up to me I'd cut the grout line width in half (or more) from the picture you posted. Those are too wide and with the grout color contrast breaks up the slate and looks busy. At a minimum go with a darker gray or complimentry grout color.
Oh and $6.00 sq/ft sounds pretty good as long as they have experience laying this stuff. I would also suggest you spend the extra $ for gauged slate for flooring applications to avoid tripping points.
Good luck!