How to override HTTP request verb in GAE
Calling the handler from initialize isn't the right way anyway - if you do that, the webapp will then call the original handler as well.
Instead, you have a couple of options:

You can subclass webapp.WSGIApplication and override call to select the method based on _method when it exists.
You can check for the existence of _method in initialize, and if it exists, modify the request object's 'REQUEST_METHOD' environment variable accordingly. That will cause the WSGIApplication class to execute the method you choose.

Either way, take a look at google/appengine/ext/webapp/init.py in the SDK so you can see how it works.
In the context of a Google App Engine Webapp framework application:
I want to changed the request verb of a request in the case a
parameter _method is provided, for example if a POST request comes in
with a parameter _method=PUT, I need to change the request to call the
put method of the handler. This is to cope with the way prototype.js
works with verbs like PUT and DELETE(workaround for IE). Here is my
first attempt:

class MyRequestHandler(webapp.RequestHandler):
   def initialize(self, request, response):
       m = request.get('_method')
       if m:
           request.method = m.upper()
       webapp.RequestHandler.initialize(self, request, response)

The problem is, for some reason whenever the redirect is done, the
self.request.params are emptied by the time the handling method(put or
delete) is called, even though they were populated when initialize was
called. Anyone have a clue why this is? As a workaround I thought I
could clone the params at initialize() time, but .copy() did not work,
and I haven't found a way to do that either.
Update: I received a very helpful response from Arachnid. The solution I ended up with uses a metaclass. It is found below.