Just would like to add that it might be possible to get your H1b approved with a start date earlier than October 1. You probably do not fall under the cap since you were in H1b status before (see item b below).
Acording to AC21, H1B workers in the following situations will not be subject to the annual H1B quota
a) Persons employed at a university, affiliated non-profit entity, non-profit research organizations, or government research organization;
b) Persons who have previously been counted against the H1B quota (a person would only be counted once against the cap unless s/he has a year outside the U.S., thereby resetting the clock on the six-year limit.)
c) Physicians who obtained a Conrad 20 waiver of the J-1 two-year home residency requirement; Extensions of stay for those already on H1B status;
d) H1B amendments with the same employer which are not requesting an extension of stay;
e) Change of employers by a person already on H1B status; and
f) Persons already engaging in H1B employment who are applying to work concurrently / simultaneously for an additional employer while maintaining their current employment.
