I was able to reposition the fender on the orange bike which seems to have fixed the problem. The weird part is that it seems like the fender was in the wrong spot all along. There is a bracket on the fender which it bolted to a spot on the frame/rack. The bracket is on the front side of the frame bar.
Here is the bracket on the black bike which I did not touch.. The bracket is bolted to the front side of the frame.
See how badly the fender sits around the wheel, and how far forward the wheel is given the remaining space in the dropout to move it back. Tough to see in the pictures, but the fender is misshapen. The fender is bulged out (in width) by about 1/4" (7mm) in front of the bracket.
I repositioned the fender on the orange bike so the bracket is to the back of that bar. This fender is not bulging, but I did not measure it before moving it.
And see how much better the wheel fits, still lots of room in the dropoout for rearward motion.
The sad part is that the bracket is shaped to be on the front side of the bar, so I had to bend it a bit, being careful to not damage the old plastic, it already had some stress discoloration before I started messing with it. I still need to tap the top down to be flush with the rack.
The tire was rubbing right under the white HON sticker on the fender. Moving the fender has fixed the rubbing. I don't think the chains are stretched. But I'll check them later using Sheldon Brown's method.
Here are pix of the complete bikes for reference. The orange one is in much nicer shape. The black one will be improved once I change the fender and move the wheel back a little. The black bike has a SunTour version of the SA 3-speed with date code of 6/81 and the orange one has a Sturmey Archer hib with date code 1/84.