That is not a direction I have seen web auth used in before, though I don't see any coarse reasons it wont work.
Web auth is a rather advanced configuration, and not something I would think is possible in this medium. This is doubly true since any walkthrus you find will be tailored to outbound traffic.
For example you are going to need to SAT HTTP(S) traffic from your additional public to the WAN IP of the DFL so that the users will even be able to see the web auth prompt.
For this to work optimally you are going to want to do this only for a service that is viewed through an HTTP browser (you hid what you service was so I don't know if this is the case) or you will have to log in with your http browser and then start your separate service.
Get yourself a competent phone support agent by calling in, if they will even help you write something this crazy, that really is a better option for you.