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.
I'm thinking boldly here. The French are able to peak at 200-230mph on operating trains running on conventional track. The Japanese and Chinese can push Maglevs up to 360+ mph. As a "disruptive" technology, 300 mph seems like it's attainable or at least worth considering.
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.
It's pretty silly to compare the average speed of the Shanghai Maglev. It's like a 7 minute trip with 1 minute at top speed. There's several, traditional HSR, routes in china with faster average speeds.
The Paris-Lyon TGV averages 140MPH. Wuhan-Guangzhou managed to average 195, but was reduced to 186. Beijing-Tianjin 146. Japan has 130-145MPH. So:
* 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.
Once again: I was comparing the peak speed of one rail line to that of another. Read in context. This snark doesn't even make sense on this part of the thread.