I had a feeling Markus would chime in, I remember him going over this a month or so ago but couldn't find the post.
Yea it seems to run like that, a particular odd model or version bike that you don't see for years suddenly pops up and then there are like three in within a couple of months of each other pop up randomly.
To the OP, the bummer is the particular brake caliper used has become a tough find. Problem with late model calipers is they dont seem to make one that has a backing plate that has threaded holes and rather they are bolt thru which causes a spacing issue since that setup is more commonly used in other types of applications. Bird even had their own backing plates cast for some reason on those bikes, if you ever find one it will actually have the bird name cast into it. Not sure if that means that they are cast thinner by a little bit or not compared to the other 200 series K&H/H&H backplates or not, only seen them in pictures.
I would consider a clutch brake to get you going and then watch for a caliper in your spare time if your current rear wheel/sprocket is in good working order if you are wanting to not alter the bike and try to actually save originality of the bike. The next version Golden pintos actually got a clutch brake along with a scrub (they also beefed up the headtube and extended the wheelbase). Its not ideal, its wear and extra heat on your clutch when its your go to full time use brake and if you loose a chain, you loose your brakes but they usually do brake good with them when setup properly.