If SM has not given you a definite date, and you know for certain the contractor they will use, I’d ring them to find out what’s happening, and book them to come earlier if you can, then let the strata manager know they are booked in.
Firstly, they probably won’t take a work order from an owner. Secondly, you can only go ahead and organise repairs in an emergency – and this probably doesn’t qualify.
Better to apply for mediation at Fair Trading with a view to getting orders under section 232 to get the owners corp/strata committee to get the work done.