I would go about it as a module; there is no reason to create a completely separate module package, you can create a separate module as part of a larger package (several core projects do this so you can look at some of those for examples on how to build the manifest file -- see the Forums module). 

For your registration module, by all means only put the fields that are required by DNN (username, password) and then the ones you want.  There is no need to include the full package (all the profile fields, etc) if you don't want to.  Just go for a bare-minimum that you need. 

Overall the premise is "Do all the customizations through a module" since that allows for upgrades with minimal amount of work.

Does that make sense? 

What are the fields?  Are they ones you had in the registration process or are these fields that are otherwise required?  If they are otherwise required you could a) include them in your registration or b) mark them required in the profile properties section and then in user settings mark "require valid profile for login" so when they next login it requires them to fill in that information.  Or maybe I'm reading this differently -- you have two required fields that they need to fill in but you don't have somewhere to put them?  If that's the case, put them in the custom profile properties (Users-->Manage Profile Properties) and then in the sample I emailed you I believe it shows how to fill info in for custom profile fields (such as their special "ID" you mentioned).

As for login -- I'd create your own login module (can be part of the greater package here) that checks the logic to log them in AND checks the "ID" to make sure it is valid and, if so, logs them in.  You can slap that on a page and then in the Site Settings you set your login page to that tab you create to put the module instance on.

As an example for logging them in, use DotNetNuke.Security.Membership.UserLoginStatus (enum) and DotNetNuke.Entities.Users.UserController.ValidateUser to validate the user and then DotNetNuke.Entities.Users.UserController.UserLogin to actually log them in.  Then proceed to redirect them as necessary (redirection is necessary so the cookies get set).

Hope that sets you in the right direction to complete your project.