Removing scratches from travertine

I have laid some filled travertine tiles on a kitchen floor and they have been sealed and grouted. I now need to remove some surface scatches caused by manoevring units over the floor.

Does anyone have any good ideas for removing scratches?

My initial thought was some mild abrasive (maybe Jif type bathroom cleaner or T-cut) on a polisher?

These are only quite shallow marks but they are quite noticeable when the sun shines. (so maybe not that much of a problem in the North West!)

I worked with a guy who was laying a large travertine floor in march and he polished out scratches with different grades of pad,this was before sealing though.You would probably have to remove the sealer then reseal after polishing out the scratches.
Not sure you could single tiles depending on size,big possiblity of it turning out patchy.

Many thanks for the suggestion.

I have found another idea which works quite well.

I have a small diamond stone which I use for sharpening silicon carbide router bits. Rubbed on the travertine, it takes just the right amount off and doesn't seem to affect the surface much. Doing it by hand is fairly hard work but you don't take too much off at once