After several days of relentless dialogue with an assortment of shade-tree persuasion devices, the half-round brass rod finally submitted to circularity. Here it is free-standing, in position on top of the banjo pot, and as seen through the translucent banjo head.
In a Ludwig banjo, shown here, head vibrations are transmitted via a wide collar down to a base where you see the tension screws going through it. The top of the pot curves up under the head, but does not touch it. My idea was to use the half-round ring to extend the pot up to contact the head directly. The good news is that as expected this makes a difference to the tone; the bad news is that it wasn't necessarily an improvement — the thing still sounds pretty ricky-tick.
I doubt that I will repeat the experiment, but just in case somebody else is trying to make a ring out of half-round, here's my thoughts in retrospect: first, brass is springy, so it has to be over-bent. My first attempt involved a 4.25 inch radius armature and only gave me a 5 inch radius curve. Second, an armature to bend the rod over should be made of metal, not wood, and it should have a flat side against which the flat of the bar can be firmly clamped as bending takes place. And you need an extension arm about 3 feet long for enough leverage: just grabbing the unbent bar worked for about 10 degrees of arc, then I had to resort to a power-pull for the rest of the circle. Might use a 1/2" id pipe with set-screws to keep the rod aligned inside it.
Thanks for the suggestions and encouragement. By the way, the anguished-moose expression is going into my permanent collection...
LFMiller (Floont)