Here is the Google+ invite workaround I just found: https://plus.google.com/u/0/me
That's the link to your own profile while logging in to Google+. Using that link should take you to a sign up page. Let me know if it works for you!
UPDATE: This apparently did not work (except possibly in a handful of cases).
Here is a link that will give you one of my 150 invites left.
Update: 141 invites left.