You cannot force a lender to foreclose on your or anyone else's schedule, and continuing to pay HOA fees under the circumstances you describe seems pointless. While the banks are not required to accept it, you could consider recording and mailing them a "deed in lieu" with the keys, and moving out. This assumes there is no equity in the property. You should consult with local counsel before making your decision.
Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
Mr. Miller is correct. Another option may be to find a potential purchaser for the property, or someone who would go through a short sale.