Should I withdraw B1 while an employer files for H1

Hi all,
I was employed on H1B and I was laid off on 11/10. My H1b dates are valid until 2016 (however the previous employer revoked it). I have my 1-140 certified in Eb3 category. I applied for B1 on 11/14 and still waiting to hear back from USCIS.
Recently, I have accepted an offer from a University to work as a post-doc.

University want to apply for H1. They told me I have to withdraw B1 application and leave the country. They will apply for H1 petition and if approved, I would need to apply for H1 visa in India.

I wanted to seek a second opinion. I am concerned if I withdraw B1 now, and leave USA, and their H1 gets denied, that mean Ii will not be able to come back and search for jobs that I could otherwise do while staying here (provided even b1 gets approved).

It seems that B1 could take until March and H1 decision would be faster (assuming premium processing). Can I request to withdraw B1 at the time of filing for H1 or after the decision on H1 has been received? If H1 is approved, could I start working with approved petition and obtain a visa stamp later when I travel or I would still need to leave USA to obtain stamp before I could start working?

Any comments/tips are appreciated.