Maybe try a floor cleaning Company, some clean tile & natural stone.

I have a huge stone FP in my home it backs oonto my kitchen where my range is . I spary with TSP and hot water wait 10 mins. then rinse off with a spary of clean water and vinegar and dry with old towels . Makes very liitle mess and the whole, not just the kitchen wall, takes about 2 hrs max. My FP is 10 x8x4 ft .I do the kitchen part about every 2 months takes 1/2 hr. I just put some old towels on the floor to catch the drips When I did it the first time it took a really stiff brush and elbow grease so yes pretty messy thta first time but so rewarding to see the difference not just mostly yearly for the LR side.