Si
I find watermarks in this environment respond best to LM cleaning.
You say you have a rotary. What speed? Just a brush? Or a drive board too?
Do you have any "soft" floor polishing pads?
Failing the lack of a bonnet, I'd be tempted to use an encap solution (or a shamppo at a push) sprayed on and worked with a white floor pad (1st choice) or a rotary brush. Some encaps can be a respiratory irritant when sprayed, so beware.
If you must go rinse/extract, lowish pressure and extra vac strokes, speed dry if practical. Most good quality alkaline presprays should be OK, acidic rinse is good.
Safe and happy cleaning

Ken