The best way to speed trains up is to eliminate time going 0mph. Less time on sidings waiting for freight trains to pass. Things that make stops shorter: level boarding, eliminating power changes, more doors?
The second best way is to spend less time going slow. Fix slow turnouts, straighten curves, and *accelerate faster after stops.*
On that last one, why is Amtrak so stuck on the idea of locomotives pulling unpowered coaches? All the horsepower in the world can't overcome the physical constraint of adhesion when accelerating from a stop. Adding more power to a single locomotive just changes the speed at which acceleration changes from adhesion-limited to power-limited.
Powering more axles is the only way. This can shave 2 minutes (or more) off the schedule from each stop - even when powered by diesel.
All of the corridor trains that run south of Washington Union Station should be EDMUs - the Virginia Regionals, the Carolinian, and even perhaps the Palmetto. This technology is commonplace overseas.
Long distance trains can keep the locomotives.