The RTC-like idea floated today fills the role of most of what you propose.
Yes, I hate the idea of Gov’t stepping in at any point, but this is a gov’t created problem to begin with.
Carter’s CRA and Clinton’s subsequent hardening of CRA rules, combined with Dhimmi controlled crony handling of Fannie and Freddie caused this problem.
Soak up the non-valued sub-prime debt (at a discount to be repurchaed 5 years from now (with interest) by the banks who decide to sell to the new RTC) and give it a value.
All the other mortgage backed derivatives will then have a value based on the “full faith and credit of the United States.”