I'd recommend heading to Aguas in the evening and spending one night there. I did this in October and it's great to be able to get in-line to go up to MP early in the morning (e.g., 4am) depending on how crowded things are.
I'd recommend looking around for a decent room in Aguas or just planning to sleep in a hostel-like environment (and only spend $10-20 for the room).
I'd suggest taking a mid-afternoon train back to Tambo so you have plenty of time to see MP early in the omrning, sunrise, walk around and then jump back on the train. I left my stuff at the Tambo and just took a backpack to Aguas Callientes.