Since nothing you tried removed the grout haze i d guess that the slate probably wasn t properly sealed before the grout was applied.
Cleaning grout residue from slate tile.
Protect your hands with rubber gloves and dip your cheesecloth or terry cloth in water.
Wring thoroughly as too much water can damage.
How to remove grout haze from a slate floor 1.
Normally a scotch brite pad water and a little rubbing will remove grout residue and the hazy appearance it causes.
Work on three or four.
Remove grout haze with water and cheesecloth.
Pick up the dirty water with a clean grout sponge.
Use another clean sponge to rinse the scrubbed slate tiles with.
Clean the floor sweep or vacuum the floor thoroughly then wet mop the tile to dampen it.