Now to answer my own question.
I scoured the web, both the COW and Adobe forums, as well as a few other locations.
It turns out that setting Media Encoder to Square pixels does not actually convert non-square source to square output – it merely encodes a square pixel movie that contains non-square pixels. I think. Adobe does not make it clear what it is actually doing.
What you need to do is make a sequence in Premiere (or a comp in AE) at the PAR and video size you wish to export. Put your content on the sequence, and then export to the same settings. That works well, although there remain some variations, such as interlacing.
In this particular project, we had 720×480 widescreen sequences (non-square) and we needed to make 850x480ish MP4 with square pixels for upload to Ooyala. I opened a demo account so I could test various settings. Once you realize that 720 non-square pixels becomes something around 854 square pixels, you stop worrying that you are stretching the width – you are not.
Exporting from the native sequence directly to MP4 with square pixels resulted in a blurry image and an error upon Ooyala encode.
You need a sequence set to your output format. So I exported an intermediate AVI native file from the sequence, then imported that onto the export setting sequence, export with the same settings as the sequence, and we are in bizzness.
2nd project was cut at 720p. Since 720p is already PAR of 1 (square pixels) I can export that directly to a square pixel 850wide video size, and the results are also excellent.
So rule of thumb – garbage in, garbage out. Square pixels in, square pixels out. Non-square pixels in – non-square pixels out. Non-square pixels contained in a square pixel movie equals a mess.
Adobe will convert, but only by putting non-native video on a sequence. So when you choose a sequence preset, or make your own, it adapts whatever you put in that sequence to that setting – though not in real time on many systems, which is why things stutter.
Learning never stops – thank goodness for that.
Mike Cohen