Sorry for taking so long to get back to this thread but thanks for all the replies!

I think my plan right now is, at the very least, to exit HND and take the monorail down to Hamamatsucho. Unfortunately, it looks like the express/limited service trains don't run so early in the morning but it still seems like that if worst comes to worst, I can at the very least get to Hamamatsucho and back. As for the rest, I'll do my best to hit up Tsukiji via the Oedo Line, but may walk depending on how much time I have as Google Maps is stating a walking time of twenty minutes or so. If not, my other idea is to just walk around the Hamamatsucho and Daimon stations just for a small sense of being back in Japan again.