Ok ... cookies? You're going to need transference somehow. Why are you afraid of passing the session id in the QS? Could you fake it? Encrypt it? Change it temporarily?
Another alternative would be keeping your sessions in the database, but AFAIK the browser still has to wear a name tag ... I'm not the most experienced in the bunch here (hello Weedpacket, bradgrafelman, and a host of others), but I'm not seeing much way around this.
The only other thing I can think of is some sort of AJAX, SOAP, or XML/JSON service that kicks off in the event of a "site switch", but I've nowhere near enough details to tell you exactly how that might be accomplished.