You should apply now with the I-539 as it may take a few months. Also, you may be able now to find a new sponsoring employer and immediately switch over to a new H-1B visa. (p.s. - the new Rubio -McCain-Schuimer bill would permit H-4 spouse a work permission, tell that to your husband.)
Change of status from H-1B to F-2 will not be a problem as long as you file the request timely, i.e. before the expiration of your H-1B. Changing back to H-1B again will depend upon lot of factors, i.e. how much time you have left on H, when the H-1B petition is filed, whether you will be subject to cap or exempt. Dealing with United States Citizenship and Immigration Services is complex, but if you have an experienced immigration lawyer, that complexity is exponentially reduced. Please consider hiring an immigration lawyer. Good luck in job hunting.
Going on F-2 upon termination of H-1B may not be a problem. However you will not be able to get back on H-1B until the F-2 is approved which may take a couple of months. When looking for a job let the immigration attorney know of your pending change of status. The attorney may seek consular processing for your H-1B.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.