In my experience the only way to achieve an overall even aesthetic appearance is to strip the whole floor and start again. Trying to mess around with sections is more time consuming.
I would scrub using PSRP Heavy Duty Tile & Grout Cleaner coupled with PSRP Hone 320 Honing Powder, Scrub it in using a Rotary, extract, Rinse, and extract again with a wet vac. Check it for appearance then allow to thoroughly dry. Then seal with Miracle 511 H2O if you want it the same colour or Miracle 511 Seal & Enhance if you want a wet look.