How To Abort An ASMX Request Based On Logic In The Constructor

I have a common base class from which all my ASMX webservice classes will inherit. In the constructor, I want to do some common authentication checks; if they fail, I would like to halt processing right away (subclass's code would not get executed) and return a 401-status-code response to the caller.

However, the common ASPX-like ways of doing this don't seem to work:

Context.Response.End(); always kicks back a ThreadAborted exception to the caller, within a 500-status-code response. Even if I explicitly set Context.Response.StatusCode = 401 before calling End(), it is ignored. The result is still a 500-response, and the message is always "thread-aborted-exception". MSDN suggests I use HttpContext.Current.ApplicationInstance.CompleteRequest() instead. However, this does not stop downstream processing: my subclass's functions are still executed as if the constructor had done nothing. (Kind of defeats the purpose of checking authorization in the constructor.) I can throw a new HttpException. This is a little better in that it does prevent downstream processing, and at least it gives me control over the exception Message returned to the caller. However, it isn't perfect in that the response is still always a 500. I can define a DoProcessing instance var, and set it to true/false within the constructor. Then have every single WebMethod in every single subclass wrap its functionality within an if (DoProcessing) block... but let's face it, that's hideous!

Is there a better / more thorough way to implement this sort of functionality, so it is common to all my ASMX classes?

edit: Accepting John's answer, as it is probably the best approach. However, due to client reluctance to adopt additional 3rd-party code, and some degree of FUD with AOP, we didn't take that approach. We ended up going with option #3 above, as it seemed to strike the best balance between speed-of-implementation and flexibility, and still fulfill the requirements.