Over the past 6 months, I've tried for an E-2 visa twice and was denied both times. Subsequently, I made the decision to return to school but I'm concerned that the E-2 denials would make my F-1 visa application seem desperate.
I'm under the impression that as long as I do not officially/legally close down my business which I applied for me E-2 visa with and provide documentation to back that up, there will be a heavy suspicion that I would be working illegally while under the pretext of being back in school. I do not wish to close down my business as I hope to keep running it AFTER my second degree, and my idea is to provide an employment contract for an operating manager which would clearly state that I would remain a passive owner and not be involved in operations.
Is that feasible?
To avoid you a huge exercise in futility based on your facts, I would strongly recommend that you look for another country to immigrate aside from the US. You seem to have, alas, burned most of your bridges with the "gate keepers" (consular officers) already.. It is highly improbable they will agree to issue you an F-1 after two E-2 refusals.
Facts, as relayed by you strongly indicate a future denial even if everything submitted correctly the third time for a simple, and easily understood rationale: you have created a documented evidence of improper submissions which will not be cured by the third, no matter how flawless it may appear. That is, of course, my personal opinion and you may pursue that venue further with a willing counsel.