All of the initial learning and review was done with me at the piano. I knew we had to introduce the tracks well before tech week so the cast would start getting used to them, but I also didn't want to move away too quickly from working with them on the piano, since there are advantages to voicing chords in certain ways, playing melody for guidance, etc.
We managed to get the scheduling right in this regard. We also were blessed with a devoted cast who took our warnings at the very start of the show to heart ("This is a difficult show! You have to do your homework! You need to make this show a priority!"). Thanks to them, we stayed on schedule.
We had the cast do most of the songs "on their feet" (i.e., with all the blocking) but to the piano first, so that Jessica could straighten out any major blocking issues (and so the cast could start the process of integrating singing with acting).
About two weeks before tech week, I brought my gear down to rehearsal, and we had the cast start singing and acting to the tracks. Unfortunately, it seemed that their "fear" of not being able to follow the tracks began to dominate their peformance, so they became less like actors and more like hesitant singers. We decided to abandon the acting portion for a couple of rehearsals and just get them familiar with the tracks, and then bring the blocking back into play. This worked out much better.
Even with the rehearsals we had been doing with the tracks, going into tech week, we weren't quite sure if the show was going to open with a fluid sounding cast. A great deal was riding on their shoulders and expectations of the director and music director were high!