Sounds like it may work, but I would not use the steel wool. Some of the fibers may get stuck in there. 220 sand paper.
Kind of like when you put the first sealer coat on before you poly. Just sand it smooth. To clean the top, I would try denatured alchohol with a rag.
Maybe you can try just one table first...on an off night?
Another thought... they have to close for a day sometime. Vacation? New years Day?
Those tables are gonna still be kind of Gummy even after one day.