Fortunately for me, my current office (like the former Menlo HQ in Redwood Shores) has showers in the building. So I'll pack stuff up tomorrow morning when I get up, move as much of my things to the van as possible, head to the office early, and shower there before going to work.
Oddly enough, I noticed that they just today raised their "headline" rate on their sign by $5/night. Well, it's still cheap, but I would hope I could get a shower without scalding myself.