Rotted floor joists - is this a viable solution?

We have an extension that is built on to and spans the back of our house. The extension sits on pillars and it has a 2.5' crawl space

The problem that we have is with rotting, compromised and/or failed floor joists and support beams on this extension of our house.

A structural engineer has proposed that we lift jack the room until it is level and then he suggests that we open or remove floor boards in order to fill the crawl space (approx. 38' x 8 x 2.5") with concrete. He tells us that this would encase the rotted wood and once dried, it would become a solid foundation for the room. He feels that this would be a better and more cost effective solution than to try to replace compromised rotted beams, joists and floor boards or to tear down the structure and rebuild it.

This extension is open to the back part of our house and so, we need to do something about this before the snow falls. We would like to know if anyone thinks that this may be a viable solution.