Put it all in a idiotically long tunnel, 100% separate from other services. Including four track tunnels to allow for passing. Simple. Hilariously expensive. Absolutely impractical. Weatherproof.
But actually .....
Isn't the real problem here that you have lots of incredibly old infrastructure, joined together in various unusual and not ideal ways, running at virtual capacity from the off ?
It's easy to forget this project was originally called Thameslink 2000, it is utterly incredulous that 18 years after the project was supposed to be delivered initially, GTR/Network Rail/DFT (and for DFT to stand back and point the finger at either party is absolutely crazy) did not produce and staff to a draft timetable a year / 18 months ago. This was always going to be such a momentous change that some staffing slack / wasted staff time was inevitable, and DFT should have absorbed some of the costs of delivering a change they initiated efficiently.
But broader than that, rather than trying to find bits of old railway to stitch together to form major parts of the capital's transport infrastructure, wouldn't we be best to think in Crossrail type terms, and be honest about the costs ? These bits of infrastructure (ECML, MML, WCML) are running at capacity. Build an entirely new route from A to B, with links to existing infrastructure at either end. With inbuilt recovery routes (4 track). Phenomenally costly, yes, but surely all we've managed to do here in the 25 odd years of this project, is to create a pressure point so densely operated that a single point of failure will produce carnage for thousands of people.
Aside from anything else, there is the target to build tens of thousands of new homes across the south east in the coming years. In X years time, Thameslink is full and standing, where does the next capacity come from ?
Until we have realism in transport planning, what hope is there to avoid further debacles ?