Renovations: Textured Tile

I have mentioned textured tile in a few posts now and I have to admit something - my opinion of it has changed.  I had a run-in with some textured tile about a month ago now and it has been annoying me ever since.  Luckily I have also learned a valuable lesson.
Don't use textured tile in high "dirt" traffic areas, for example, the kitchen.  I have a client with a gorgeous house.  It's really lovely.  They also happen to have a kitchen full of textured tile.  When I first started working for them I thought the textured tile was wonderful (it is in other areas of the house).  It cleans easy, it looks good.  What more could you ask for?

Then I got to know the floor a little better.

I began to notice that deep in the grooves were masses of little black spots.  I didn't like them and decided that the floor would look much nicer if they were gone.  Here's the problem.  The nature of "dirt" in the kitchen has created a sort of super glue out of the black dots.  I started with a rough scrubbing squeegee mop, nada.  I then spent a full half hour scrubbing at the dots in probably a meter square area (after soaking in a soap solution).  I got them out alright but their kitchen is huge and I now have my work cut out for me - damn those black dots taunting me!

So what is the lesson?  No textured tile in the kitchen or in any high-traffic area where lots of stuff gets dropped on the ground and then ground in.  A patterned tile with a smooth texture is much, much, much easier to clean.

I will write more if I figure out a solution.  I am worried that I am going to have to go chemical, but we will see.