The upshot is that I've bought a 26 x 1-3/8 chrome replacement fork. These forks can be bought on Amazon or ebay for relatively little money, are made of mild steel, and are reasonably solid. They have a "retro" look to them, which can be made to work with this bike.
More bad news came in the form that the headset on this bicycle was an oddball dimension. I could not even get vintage, mainline "American" sized parts from the 1950s to work. Apparently this bike used some sort of other size that is neither the common "vintage American" size, nor the more modern "ISO" size. I ended up removing the frame cups and headset, replacing with a Wald unit, which is fitting given so many of the parts on this bike were already made by Wald.
In the end, this bicycle is headed a little more toward "custom" than the usual build, but so far that seems alright. The bike has a little of the look of the earlier lightweights, which often had plated forks mated to wildly painted frames.
Progress continues with more assembly. I've nearly gathered all the parts at this point.