grouttile
A bathroom floor's grout is to be whitened. A Google search listed all sort of remedies including bleach, vinegar, peroxide, commercial solutions.
I would like to avoid having to use a brush and apply a solution with a mop or similar. If you have experience excellent success with a particular solution, I'd appreciate hearing from you and any lessons-learned. Thank you
Don't re-grout, clean it! Talking with a Home depot guy last year about this and he was amazed I still had to use a brush. He shows me this stuff called oxygen bleach from Ajax. This was literally the easiest method I have ever used. Make a solution with just enough hot water to dissolve it, apply and let it sit for 15-20 min and mop off. That easy. I will never use a tile brush again. Once you get it sparkling white, you can upkeep it my adding a small amount every time you mop and you will have pearly white floors forever.
In the to-do section of the care instructions you posted, it suggests "Use an all-purpose, non-oil based household or commercial cleaner." OR, it says, you can use vinegar/water.
I think you are over-analyzing. The normal floor mopping solutions like Pine-Sol or a Swiffer will work fine. Just don't use anything abrasive that will scratch the tile or an aggressive bathroom "tile/grout cleaner" that is meant to bleach and renew grout that is stained.
If you're concerned about a particular cleaner, you could always test a small section that is out of sight. You can also apply a "grout sealer" solution over the grout lines. This is tedious, but can help slow down staining of the grout.
Best Answer
I'd try a good bleach soak first. I have mosaic tile countertops with white grout, and a good bleach soak removes any of the evils my wife can dole out...