Actually, both the Eagle and Sunset were early at nearly every major time point, which led to us having to "wait on time" for up to an hour at some points. This is because of massive amounts of padding ("recovery time") that Amtrak has inserted into the trains' schedules in order to deal with delays that the host railroads inflict upon them. While that helps on-time performance, it also leads to being turfed out of bed before dawn, as the car attendants want to go home so you can't stay aboard until, say, 8 AM.
Lisa and I groggily made our way to the subway and up to our hotel near MacArthur Park. My Priority Club Platinum status was worth platinum today, as they found us a room and let us check in at 7 AM instead of having to wait until 3 PM. We were in no shape to do anything and would have been miserable much of the day. Instead, we checked into our room, dropped our bags, had breakfast (admittedly, we've managed an extra breakfast out of this), then went back to the room and did very little. Lisa slept for a while, and while I would have liked to have done so, I had huge amounts of e-mail to process.
We have no firm plans for our two days here in LA. We mainly planned this hotel stay because we figured we'd not be worth a whole lot if we'd transferred straight to the Coast Starlight this morning. But if we just lay around and sleep, or do some minor walking around or something like that, it will be enough for us.