Well, replying to myself again... this time with possible resolution. Perhaps this will help someone else, though our situations are all different.
I create Twitter Cards via a Wordpress plugin. I've found that the message must contain a shortened URL. Typically the post-to-tweet contains: #title# #tags# #url#. If I leave out the URL the Twitter Card doesn't get created; I only see a regular Tweet.
For those who use the WP to Twitter method I've found the best plugin to be "WP to Twitter". It's API based so you'll need an app. I've tried other WP plugins, but this one seems to work consistently.