I think Dave and Darrel nailed it . . .
The Hickey nut has a 3/8" thread, which is a common size for gas service. Lowe's doesn't carry anything with that size thread in a mounting bar.
Currently I'm stuck, because the Hickey is stuck. I'm pretty sure it's fused by rust. I can't remove the canopy or the sleeve it surrounds because neither can get past the Hickey. The sleeve appears to be brass, but that's all I've been able to identify thus far. The canopy is definitely cast something, but I don't know what yet. Anyway, I can't rewire if I can't get the Hickey removed -- unless fishing new wire through from the top may be possible with the mounting assembly remaining intact.
I sprayed PB Blaster where the Hickey threads onto the pipe and am letting it soak in overnight. If I can't get it to budge, I think taking a shot at pulling new wires through from the bulb base is all that's left to try before handing the job over to a professional.
So Dave, are you suggesting that I punch out the rear slug on an electrical box and mount a 3/8" nipple onto it there? As long as the box is securely fastened, that sounds like a fairly simple solution to the mounting issue. My preference would be to use a mounting bar, but I don't think I'll find one with a 3/8" thread. The reason a bar would be better is that they usually have long slots for the mounting screws that allow for side-to-side adjustment. The current box for the front porch fixture is close to the edge/corner of the wall, and the large canopy on the torch fixture would likely protrude past the edge. I was hoping I could rig a mounting bar as far to one side as it would go, resulting in the canopy moving far enough in from the edge to correct the problem. Another possibility is to find a box with more than one rear punch-out so I could mount the nipple off center. The canopy is still large enough to hide the box behind it.