It shouldn't even need to be high-speed rail. NYC to Miami is just a bit over a thousand hours, and at 15 hours (6pm to 9am), that's an average of about 70mph.

It shouldn't even need to be high-speed rail. NYC to Miami is just a bit over a thousand hours, and at 15 hours (6pm to 9am), that's an average of about 70mph. The real speed of the train would need to be faster, accounting for the fact that the route is not direct and has stops in the middle, but it should be doable with "regular" train technology.