If you know for certain that the 96BPM tempo is what the drummer was actually working to, the procedure I gave will work. But if that tempo was just an estimate, you might do better to count out 8 or more measures while listening to the drums, and then Shift+M with the Now time on that transient to set the actual measure and beat by what the drummer played. That's the real intended use of Shift+M.
Incidentally, that tempo ratio is very close to 48/44.1kHz. So I suspect this is all due to a clocking issue... or maybe you already knew that, and that's how you calculated the target tempo...?