Sigh.
Well, I have to retract some of what I said. It is true that I am getting a signal out of the converter using the new SCART cable now. At first glance, I saw what looked like a little RF interference and was planning on swapping it out with a better cable. I did not continue to work with the computer, though. So when I sat down a little longer, I noticed the slight RF interference degraded into a strong image instability problem. It is hard to describe, but basically the image is filled with mangled graphics and the original wavy interference lines. In short, it is unusable as it appears.
Still, the fact that I am getting an image out of the converter now would seem to indicate that achieving a stable picture from the converter is possible with the right cable-- one made to certain specs perhaps?
@djos, I still think you're better off with a Retro Computer Shack cable, but you may want to reconsider after this update.