I'm aware that you can configure by file type (first line below) but i'd like to be more specific. I tired the 2nd line below, but didn't seem to work. Am I doing something wrong?
#AddHandler server-parsed .html
# Would like to only parse *.dyn.js, instead of all *.js files
AddHandler server-parsed .dyn.html
It is not how you should do it. Here's why: according to the mod_mime documentation, apache treats the all of the sections of the filename which begin with dot as an extension. In the example you provided, if you have a file, say, default.dyn.html, it is treated as a .dyn and as a .html file simultaneously. If simultaneous handling happens to be impossible, apache processes the extensions from right to left. So, you can't define an "extension" which contains a dot.
What you should do instead, it to define the "server-parsed" handler for the .dyn extension only. In this way, if you have a .dyn.html file, it will be registered to the server-parsed handler and to the text/html mimetype. Since these can coexist nicely, the file will be parsed, and will be served as an html page.