um, not to throw a wrench into the mix, but check w the AEA offices - some contracts allow a daylight day of rest rather than a day off, and a reading may fall under those rules (I tried to find my one-sheet w the rules for readings but have no idea where I stashed it, sorry) - if that's the case, given your limited rehearsal period, you can figure out when the best time would be - often it means tech days, when the cast isn't called in before 7 pm and the tech crew has all day to solve stuff (which cd mean OT for you as the SM but not necessarily).
If I find my one-sheet, I will post any info I find here