I am so sorry your father is in the hospital with COVID. How awful to have this stress on top of it all.
Praying for you and your family.
You are right, litigation may last years. My best guess is that if something happens and your father passes, you have survivors rights to the property, which creates a new ball of wax. I have thought of this with my own family and the mortgage. The lack of resolution is in itself harassing where they could have played fairly and negotiated to cure the debt a long, long, time ago.
Others may chime in on this, but you might consider converting to a chapter 7 which, if house is underwater, discharges the past due uncollectable parts. Also, in Chapter 13, another thought is they might have to sue and prove they are in fact the party that is actually "the real party in interest," meaning you can force them to prove their entitlement to collect or foreclose. Many lenders do not have such proof.