Cleaning Yellowed Slate Floor.

Hi;
I have hundreds of sq. ft. of unguaged slate floor of many densities,
originally sealed with penetrating silicone type sealer which was cleaned by
mopping with Lysol; not by me.  It's now yellowed and darker.  I want to
maintain the matt finish.

I tried and expensive chemical stripper, which still required mega scrub
work get the grime out of the pores.  I prefer to lighten rather than darker
it.

What's an inexpensive mop additive that'll brighten it over time; detergent,
vinegar, peroxide, bleach?  I'll spend a little more if you have a favorite
cleaner.

What say you?

Thanks, Heather.