Today the weather is cold and drizzling, but I couldn't stay away from doing something on the trailer.
Without taking the tarps off, I rolled up the sides a little so that I could access the side utility doors. What I found was a little wetness dripping down the sides of the trailer, but no warping of wood or absorption of the water as far as I can tell. I will not be able to examine the roof until a nice dry day, but I am 99% sure it is ok up there under the second smaller tarp.
With the side utility doors open, I found it was bone dry inside.

Very glad of that, since the electronics are in there. I did a couple of small projects with the electrical:
1) I hooked up the 1000 watt pure sine wave inverter using 2 gauge cables. It works great! About 30 seconds after turning it on, the automatic transfer switch senses the current and then turns the power on to the household 120 v AC outlets. My multimeter showed 128 volts at the outlets, so there is plenty of AC power! The inverter is now wired and ready to go.
2) I built the aluminum frame that will hold the solar panel to the roof, and bolted the solar panel to it. The solar panel can now be positioned at a ~40 degree angle, which is about ideal for this latitude when it is pointed south. The frame can also be collapsed and secured flat for travel, or for when the trailer cannot be parked pointing south.
3) I hooked the panel up to the Tracer charge controller in the trailer for the first time (wires out the door and solar panel sitting on the driveway). What I found was even on this cloudy, drizzling day, the panel outputted 28 volts. The batteries registered 12.52 volts before connecting the panel, and 12.68 after, which means they are getting positive juice from the system. It will take a much sunnier day to charge them fully, because that would take 13.5+ volts. I believe something like 12.8 volts registering from the battery after it has sat a while and equalized is a full charge.
After playing with the electrical for a little while, I disconnected the solar because I didn't want to charge the batteries long enough to accumulate explosive gasses under the tarp. (I need to buy a hole saw of the right diameter so that I can install the battery box vents soon. Until then I will only charge the batteries when I can vent the whole trailer.) Next, I buttoned up the tarps again and secured them with ratchet straps. We are still going to get 40+ mph wind gusts and scattered showers from the hurricane offshore, and I want the trailer to be ok overnight. Maybe tomorrow afternoon I can take the tarps off and dry everything out.
I'll report on the condition of the roof at that time. Thanks for reading!