Again: average speed. Peak doesn't matter. Your stretch goal doubles the average speed of one of the fastest trains in the world, running on a route built from scratch to accommodate it.
It may require new approaches. It would be a monumental engineering effort. It would probably ensure full employment for a decade or more. But I don't think it's any more ridiculous than, say, sending a manned mission to Mars.
* None of these average speeds would make Chicago-Houston competitive with air. Even if you add the hour on both ends for the air trip, the fastest train in China operating above the Chinese speed limit still loses to Southwest Airlines.
* None of these average speeds make a 300MPH average speed train any more realistic.