Well, we think we figured out the reason for LP's late night wakefulness - separation anxiety. I know, it sounds kind of weird that a little munchkin would decide that the middle of the night was the appropriate time to be lonely, so much so that it would force her little brain out of a deep sleep, but that seems to be the case.
After another mom in LP's class complained about her daughter waking at 2:30am because of separation anxiety, the Hoos did some investigating and apparently this is pretty common. A response strategy is to go into the baby's room when they wake up crying, and without making eye contact sit in the room to let them know you are there. After a few days of this, the baby will start being more confident that Mommy or Daddy are close by and a full night's sleep will resume.
The Hoos tried this tactic the other night and it seemed to calm LP enough to fall back to sleep.
Last night, after putting LP to bed when I thought she was asleep, she jumped up as soon as I left the room and started crying. This happened several times. I decided to sit in the glider in her room to comfort her. She stood up in her crib and stared at me for a while, without crying, and eventually she just fell over into the meatloaf position to sleep. Instead of risking waking her, I wanted to take some time for her to fall into a deep sleep. You guessed it, twenty minutes later the Hoos woke me up from my deep sleep.