I finally picked up one of my "grail" pens. In the late-1890s and the first decade of the 20th century, Parker catalogued and sold two non-Parker pens as "cheap, but good" alternatives to Parker Lucky Curve pens. One was the New Special for $1.50 while the other was the Silver Dollar for $1.00. Both are pretty scarce.
I now have the Silver Dollar in the collection. It's just your basic black hard rubber pen with a simple barrel imprint. There's no imprint on the nib, which looks original based on the patina on the gold and the shape. It's actually not much different from the Parker Number 1 in both size and shape. It wouldn't surprise me if all the components are the same as the Number 1, with the only difference being the lack of the Lucky Curve feed and the Parker imprinted nib. The Parker catalog notes "They are good pens for the money. Both have gold pens and screw joints, but do not have the Lucky Curve feed".
Below are photos of the Silver Dollar pen.
Below are some photos of Parker Number 1 pens. The BHR is a very early overfeed but the section shape is almost identical to the Silver Dollar. The RMHR version is later, but shows an overall similar platform.