On the surface, this question appears similar to How to add custom image tag to pagedown? However, in practice, I think the solution will take a very different form.
With PageDown, you can add an <img> tag to a text block two different ways:

<img src='myimage.png'>
Looking at the code, the first approach is handled in _DoImages in Markdown.Converter.js, creating an <img> tag with the appropriate information contained within it. The second approach is handled in sanitizeHtml (which calls sanitizeTag and uses img_white) in Markdown.Sanitizer.js.
All I want to add is that every single <img> tag that successfully passes through the Markdown has a CSS class added to it (e.g., "user-img").
So, for example, <img src='myimg.png' width='100' height'100'> would become <img src='myimg.png' width='100' height='100' class='user-img'>
Examining how Pagedown is structured, I think it would make the most sense to have this functionality added as a "plugin hook" operating at the "postConversion" stage, in my own code (i.e., i wouldn't have to change anything in Pagedown). In pseudo-code, I think the code changes to my code would look something like this:
init function:
this.converter = Markdown.getSanitizingConverter();
this.converter.hooks.chain("postConversion", userifyImages);
userifyImages(html_text):
// note: `html_text` is just a plain string
for every <img> tag that still exists (i.e., is valid) in html_text:
    add "class='user-img'" to the tag
I'm guessing that there is a relatively simple regex to be constructed based upon that rule, but I'm afraid that I've failed to deduce one.
So I have two questions:
(1) Do you think this approach makes sense, considering how Pagedown is structured?
(2) Do you know how I might create a regex that does the manipulation I'm requiring? (or, of course, solve the problem without the use of a regex.)
Thank you for your time.
 
                        
Okay, basing my approach on Pagedown's existing code, this seems to work fine.
However, I'm not overly comfortable with the regular expression:
/<[^>]*>?/gi. I'm not sure what exactly the?is doing there. Nevertheless, this appears to work.