If I do finally surrender it, how long until I have to move and what happens to all my other unsecured debt?

Trying to answer questions like this without looking at your entire BK file, including your current financial situation, is a "guess" at best. Pay an experienced BK lawyer for two hours of their time to review your BK file, ask you questions about your current situation, so you can get quality legal advice. Now is not the time to skimp!

You are so busy making assumptions like whether the court needs to approve a foreclosure and whether the bank is going to foreclose because of the substantial loss they will take, I do not see you being willing to accept advise that conflicts with your view of the world. Once the lift stay is granted by the bankruptcy judge, and it will be granted if you have not been paying the mortgage, the bankruptcy judge will no longer have any ability to stop the foreclosure. Ten years ago, lots of people assumed that the bank would never foreclose. They were wrong. In determining your Chapter 13 budget, your plan payment was based on your promise to make your mortgage debt and your HOA dues. Since you failed to make these payments, you spent money that should have been going to pay your creditors. Under these circumstances, I do not see any future in you continuing to remain in Chapter 13. You need to discuss this with your Chapter 13 attorney and be realistic.

You can always ask for a loan modification but the bank doesn't have to grant it. Since the bank has asked for relief from stay, it's safe to assume they intend to foreclose.