J,
I'm not sure what suggestions you're looking for. We support JFBConnect, which is definitely a Joomla-based component. It's not meant to be standalone, and without knowing what your 'custom' authentication is, it'd be really difficult (if not impossible) to propose any way to migrate off.
Additionally, it looks like your subscription isn't active. I'm not sure what version of JFBConnect you're using, but any suggestions I'd have would be based off our most recent v5.0 release.
In general, we'd always recommend using a CMS as the underlying system. It takes care of so much and has a lot of security built-in, due to so many users using it. If you go your own route, you're really giving up on a lot of flexibility and development that is 'free' by simply choosing a CMS.
Hope that helps, though it might not be exactly what you were looking to hear.
Thanks,
Alex