Any suggestions on the easiest way to pick through this Mail
directory to pick out
the important emails?
You can access them where they are with mutt or move them to where
Thunderbird or some other mail client can see them.
The files without extensions are mail folders. You may see
directories (folders) which may contain other files w/o extentions
that are also mail folders.
With mutt you can just do
mutt -f <path>
or start mutt and press 'c' (change folder) and navigate from there.
With thunderbird put them (with a name that isn't already there) in
the .../Mail/<account-name>/ directory while t-bird is not running
and start t-bird and you will see those mail folders with the names
you gave them. With other mail clients similar things are possible.