When my cast can't use the stage for rehearsal, our theatre's rehearsal space is an abysmal little basement room with old fashioned school-tile type floors. You know, the ones that EVERYONE'S shoes squeak on? And one of our actresses was wearing new boots. It got very distracting in rehearsal.
Solution?
Grab some spray-starch from the costume department, spray on bottom of shoes, allow to dry, viola! Much fewer squeaks! Not slippery! And leaves no residue on the floor! If it works on those tiles, it's got to work on a stage surface.
Thought I'd share!