Web client through https proxy - is it even possible?

I'm trying to post some data to a web server, but need to go through
an https proxy.  I can't seem to find anyone that's pulled this off
with a twisted web client.   I've been sniffing traffic and have it
close, but can't quite get past creating the SSL socket.  Anything I
attempt to write to the transport after swapping out the standard
socket for SSL.Connection fails the SSL handshake on the remote end.

Here's the code so far:
class MyProtocol(client.HTTPPageGetter):

    got_connect = False

    def connectionMade(self):
        proxy = os.environ.get('https_proxy')
        if proxy:
            self.transport.write('CONNECT %s:%s HTTP/1.0\r\n' %
(self.factory.host, self.factory.port))
            self.sendHeader('Host', self.factory.headers.get("host",
self.factory.host))
            self.sendHeader('User-Agent', self.factory.agent)
            self.transport.write('\r\n')
        else:
            self.got_connect = True

        if self.got_connect:
            client.HTTPPageGetter.connectionMade(self)

    def lineReceived(self, line):
        if not self.got_connect:
            self.got_connect == True
            ctx = ssl.ClientContextFactory()
            self.transport.stopReading()
            self.transport.stopWriting()
            self.transport.socket = SSL.Connection(ctx.getContext(),
                                                self.transport.socket)
            self.transport.fileno = self.transport.socket.fileno
            self.transport.startReading()
            client.HTTPPageGetter.connectionMade(self)
        else:
            client.HTTPPageGetter.lineReceived(self, line)