2 hours later...
Well, I decided to use the Sawz-all to chop off the chimney. Those last 3 screws on the fascia did nothing to loosen things up.
Finally found that the boxy section is bolted to the water tank section. I was only able to remove those phillips screws on one side though - the other side is sandwiched in a tiny bermuda triangle in the closet.
That little tidbit, combined with the fact that the water tank is actually an inch or so TALLER than the inside skin it's supposed to slide past on its way out leads me to believe that all this furniture was *built around* the water heater, and that unlike the photos at the top of this thread, I will not be able to pull it out through the side wall.
So... I've spent hours on this. Should I simply hack up the whole water tank into smaller pieces with the Sawz-all? I don't see many other options here, as I'm obviously not going to deconstruct the entire trailer to get to this thing.