You could absolutely list your property for sale as a Short Sale and get an investor to purchase the home and rent it back to you. But only if your bank does not ask you to sign an "arm's length" affidavit or does not include language in your written short sale approval stating that this must be an arm's length transaction. If presented with an arm's length affidavit, you very well could change the language of the affidavit to disclose the future tenancy, sign that and send it back to the bank.
I closed a short sale with a similar situation and with an arm's length affidavit. The seller made the additional disclosure to the lender about the prospective tenancy and the lender did not mind. In fact, the negotiator at the bank told me "the investor requires these arm's length affidavits, but we don't really care".
List your house as a short sale and disclose everything to your lender. If they agree, you're gold. If not, you are no worse off than when you started. Win-win.