1920s/30s Black and White Tile Restoration Advice Needed

[RDCoombs]

I've recently bought a house dated around the 1920/30s and found black and white tiles underneath the carpet in the hallway.

I've already cleaned the majority of the grime away, including paint marks, stiff glue and dirt, however there's a few parts I really can't rectify:

• Yellow/brown underlay shaped stains on some of the white tiles. Marks are ingrained.
• Underlay type marks to some of the black tiles, they have a whiteish hue to them.

I've used alkaline solution, No Nonsense Grime Remover and brillo parts but no matter how much I've tried I just can't get the stains to lift!

I'll attach some photos, any advice greatly appreciated.

 

[RDCoombs]

I've attached a few photos below of the pattern and issues I can't sort. Cheers!