Barry, your description of generator starting definitely sounds like a house battery issue. Doesn't sound like the batteries were up adequately to crank the generator, but when you started the Ford engine, the additional output from the alternator put you over the hump and the genny started. Since you said you've had the unit plugged in, your converter/charger should have kept the batteries charged. Easy enough to check status if you have a voltmeter. I don't know what type batteries you have--if they're sealed AGMs, electrolyte should be fine; if they're flooded lead-acid (FLAs), I assume you've maintained electrolyte level in the cells--you probably know that the FLAs are subject to boiling dry if they stay on the converter charge for an extended period without water replenishment. Regarding age--well-maintained batteries of either type should be OK at five years, but the FLAs deteriorate pretty quickly if their electrolyte drops.
Regardless of battery condition, while you're plugged in the converter/charger should be providing adequate system voltage to your 12-volt circuits, and sounds like it is. Consequently, your 12-volt overhead lights work. I would certainly agree that means your strip LEDs should be working too. I know of no reason why bad house batteries could affect just the LED strip units--they pull less current than the ceiling lights and if those work normally the strip lights should. They do have that sensitive sensing circuit for the "touch-on/off" feature, so to eliminate some crazy reason why the converter/charger could somehow be the culprit for just those lights, you could unplug from your 50 amp and start the Ford engine. Then your 12-volt circuits would be getting power from the engine alternator instead of the converter-charger. All lights should also function under that arrangement; I wouldn't expect that to make a difference, but it's easy to check.
It really sounds like: #1--you need to inspect/test your house batteries, and #2--you're just not getting voltage to that strip light circuit, like the 12-volt circuit fuse is blown. I don't know WHICH 12 circuit they are on, or if they're the only thing on that circuit, but I do know that all are on the same circuit. If you haven't already, I would carefully check fuses. You may have pulled and re-installed them (as suggested in that Facebook post), but that wouldn't correct a bad fuse.
Mike