H1B portability from exempt to non-exempt H1B

[jairichi]

Hi,

I am currently working as a postdoc in an US university on a J1 visa. I recently obtained a waiver. My current DS2019 expires by 31st Jan 2013. My current employer (US university) is filing a H1B application for 2 years validity with premium processing with a start date of 1st February 2013. Since I am not traveling to India now it is going to be a change of status rather than a consular processing (visa stamping at an US consulate in India). I have a prospective employer (a pharma company in US) who are interested in hiring me. They are willing to file a H1B application on my behalf in the fiscal year 2013 but are not ready to wait till 1st October 2013 for me to start work. My questions are,

1. Could I use the H1 portability say in May or June of 2013 to transfer from University H1B (exempt) to pharma company H1B non-exempt?

2. If yes, when could I start possibly working for pharma company?

3. And, if my H1B portability is approved before 1st October 2013 do I have to stop working, return to India, get a visa stamped and return by 1st October 2013 to US? Or I could continue working for the pharma company?

4. On my I94 the US University name is mentioned with no valid date of expiry. Will this by any chance have any impact on my H1 portability application?

Thank you in advance for your help and reply.