I remember the sawdust but not the white tile floor. I was there around the same time since I was told the bathroom was for men & women, as well as legend of certain rock star & women “jointly using” the restroom.
McSorely’s was previously a men’s only clientele and begrudged having to go coed, hence the coed restroom, or at least that’s what I was told. That aside, the place was remarkable for its history and historic wooden bar furniture with the various carvings that patrons left behind, and the bartender that looked and sounded like a time traveler from the old days.
Sorry for my rambling, having gotten carried away with nostalgia!