University H1b transferring to Corporate

Hi,
I have a question regarding the H1B Transfer. I am currently employed by a university on H1B and have an offer from a non-cap exempt company. I understand that the cap for 2006 is over, even for the advanced degree. I will really appreciate if you could tell me when can I start working. Since I already have H1B, under the protability provisions, can I start working in April 2007 for the new employer when the application process starts or do I have to wait till October 2007. I will really appreciate your response.