Rewriting parts of it will not take years. Most of it can probably be thrown away, replaced by standard components. (only talking from personal experience, sure we had legacy systems running for years).
Unfortunately that wouldn't work with this site. Between the five of us in my group we have nearly 100 years of developer experience. We've talked a lot about if there is anyway we could divest of it a little at a time or replace parts of it, but we really can't.