Well, I made it back down to the ground and I'm writing to you from an upper story of a walk-up apartment in Harlem. The entire 3,000ish mile trip took under eight hours door to door.
Getting to and from the airport on transit works differently in LA (LAX) and New York (JFK). In LA, I took the FlyAway bus from Union Station downtown ($7). This bus goes straight to LAX (no stops) on freeways with half-hour service. It's charter bus style with comfy seats and room for your luggage under the bus. You tell them your airline before you get on and they stop at the right terminal. Fast, comfy, beautiful. I really recommend this service if you live close to Downtown, Westwood, Van Nuys, or Irvine.
At New York's JFK airport, there's an elevated light rail system called AirTrain ($5). It serves all the terminals in the sprawling airport for free, with frequent, apparently 24/7 service. You only pay if you take it outside the airport on its two connections, towards Jamaica station in the north, or towards Howard Beach Station to the West. After that, for me, it was one train the rest of the way. Before long I laid eyes on one of the city's grimy-bathroom-tile-esque subway stations once again. It sounds like a criticism, but it actually made me very happy.