H1b in training to non-cap exempt employer

[MrFancy]

Hi,

I'm currently under h1b visa as a resident in medicine. However, my H1b will expire June of 2017, when my program ends. I have a few attractive offers already, but they are from non-cap exempt employers. I know non-cap exempt H1b is somewhat of a gamble (due to needing to go thru lottery), and I am considering going forward with non-cap exempt H1b first then going for NIW (by promising to work for 5 years in underserved area) if H1b does not work out.

If I do get H1b, do I need to leave the country until Oct 1? Is there anything I can do to work in the US during July-Oct?

Thanks