First, is the H job going to be cap exempt? If not, then you couldn't start work any earlier than October 1, 2013.
Second, have you talked to your foreign student adviser about the 'merits' of your reinstatement request.
Third, since you appear to be technically out-of-status, even if this were a cap exempt H .. you will need to leave the US to get an H visa stamp ... effectively abandoning your reinstatement application.
Meeting with an attorney would be an extremely wise thing to do.
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A nonimmigrant can hold multiple visa stamps in his or her passport and use those in accordance with the purpose of a particular trip. A nonimmigrant can only be in one status at the time.
A nonimmigrant cannot change status unless the status from which the change is sought is valid on the day when the change of status application is filed.
The last action rule applies unless additional H1B employment is claimed instead of change of status. This is why it is always dangerous to file multiple petitions at the same time.
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The fact that you are attempting to get F-1 status reinstated indicates you are currently out of status, as Mr. Capriotti also points out. You may have some difficulty getting the F status reinstated if you've already indictated your real intent is to work in the U.S. On the other hand, you wouldn't want to miss the H-1B cap by waiting until the F is reinstated--if it is reinstated. It seems you will need to leave the country to resolve this. I recommend getting a lawyer.
This reply is intended only as general information and does not constitute legal advice in any particular case. This reply does not create an attorney/client relationship.