Home Made Grout Cleaner

     I have a recipe for home made grout cleaner:

          7 cups water
          1/2 cup baking soda
          1/3 cup lemon juice (I used the kind in a bottle)
          1/4 cup white vinegar

     With 1,000 square feet of tile and a muddy, little dog, we have some serious grout cleaning issues here.  I use bleach and hot water for regular mopping.  That keeps most of the grout clean and bright, but there are areas that get especially dirty.  Once I used Soft Scrub®  with bleach on the problem spots.  It did a good job, but I had to rinse several times to get rid of the grit that was left behind.
     Today was product testing day for the do-it-yourself grout cleaner.  I used hot tap water and added the ingredients in the order shown above.  The addition of the lemon juice made the solution fizz.  That's a fun sound.  It happened again when I added the vinegar.  You are supposed to put this concoction in a spray bottle and squirt it on the floor.  Also, it's supposed to soak a few minutes.  I didn't have an extra bottle, and I didn't have time to fool around.  I slopped it on with a rag, waited about one minute, and scrubbed with a stiff bristled brush.  I finished by wiping to absorb the excess liquid.  When the floor dried, I found the baking soda left a film behind, so I had to rinse (only once) with clear water.
     So, how well did this witch's brew do?  I would have to say the results were fair.  The dirty grout lines were cleaner, but not like after the Soft Scrub® treatment.  On the plus side the mixture was non-toxic and odorless.  I didn't scrub very hard, and I only did one quick rinse.  I might try this method again if I had to clean up a trouble spot, and I didn't have much time.
     I'm still on a quest to either find or create the perfect product.  Any suggestions?