I would like to be able to create an URL structure where I can view my user account through:
/settings/account
and then updating through a RESTFUL controller at /settings/account/update, identical to Twitter.
except it seems I am unable to extend the Controller_Rest and have an action method at the same time. What solutions are there for this?
If you mean mixing REST and Template functionality in a single controller then no, that is not possible at the moment. It should be possible to create a base controller that does both, but I don't think anyone has merged the two...
if not, you will have to use the Controller_Template, and add REST functionality manually to the actions that need it.