Is the orientation date of your current school later than the orientation date of this school? I think I remember MSOM having a little bit earlier start than most, which would be favorable.
What I would do is give your landlord an expected signing date of after said date, for example, July 1X, and just pay the first month's deposit at your current lease, to basically "hold your spot." Then, after MSOM's orientation, you probably won't be getting off the waitlist, so you should be free to sign the lease and fully commit without worry.
You would obviously lose your deposit in the scenario you switch last minute, but a grand or two is nothing compared to being locked in for a year plus. Depending on your landlord, they might also deny the request for another individual who is ready to sign sooner, and you won't be able to move in until after you sign, but depending on how much and willing you want to go here, might be worth it.