So I tried something later in the day, I put a 26x1.1 tube in it instead of the 26x1.5 in it. I then put some air in it so that it would stay in the tire and not along the rim and mounted the tire. It was no easier to get it mounted, but at least the tube was out of the way and didn't get pinched by the irons. This tube is a little skinny for the tire, but seems to be holding up after a short ride.
This still leaves me thinking I'll try a different tire, maybe the Michelin Wild Run'r 1.1 as I said. A little pricey but not too bad. My wife suggested a new wheel. I may take her up on it with a dynamo hub. That'll make this bike a real commuter, now that I've put fenders on it, except that a battery light will actually be brighter even if it won't last all night.