I'm going to stack my field experience with fortune 500 food store floors with anyone in this industry and say that using a rotary will be like peeing into the wind. Even a cylindrical machine will miss many areas and never get under the tables, let alone the polluted base boards.
A Cimex with the stiffest tile bristles has a chance in the open field after 30 mins of dwell time. If you are staring down a medium to heavy polluted floor with polymerized grout lines you will need high Ph, citrus and oxygen. Tons of dwell time. The polymerized grout lines are the final and real challenge.
You would be shocked on how productive you can be with a blanced cocktail of dwelled chems and a simple brush like
http://www.theheavyweight.com/, then vacuum it off with a simple squeegee suction wand. A turbo will increase your times on the jobs but you're going to need more then 1000psi and more then 230 degrees to knock things out of the park.