H1B extension or J1 conversion while still working in US

[medico_in_us]

Hi,

I am currently on a fellowship in a university in the US working on a H1B Visa. This visa was exepmpt from the cap. My current employment ends in July 2012.

Now I have received an offer from a private hospital for a fellowship starting Aug 2012. I am trying to get information on two possibitilies:

1. Get my H1B non-cap Visa converted/transferred to a regular H1B and continue working with the new hospital as soon as my current one ends.

2. Switch to a J1 visa instead and work for the new hospital.

In either case, I want to be able to continue working in the US without having to go back. There is virtually no gap between the last date of my current employment and the start date of my next.

I hear that option-1 may be challenging because of the change in status of cap exempt visa to one which is not cap exempt. This is because private hospitals probably dont qualify for the cap-exempt visa. Can this be done while still in the US? Even if the transfer is done, can I not work before October like regular H1B? Is there some situation in which I can start working with the new hospital in August itself?

As for option-2 (transfer to J1 status), again I am not sure if that can be done while staying in the US and not creating any gap in employment.

If anyone has information in either or both options, please let me know. Also any advise on the pros and cons between the two options?