With the following I am done with this discussion.
The "3 hours 50 years ago" between New York and Washington was AFTER considerable money had been spent raising the maximum speed limit from 80 mph to 110 mph, or 125 or whatever. Either way, without alignment changes the difference in practical minimum run time is close to nil. Yes, much money has been spent since, mostly on upgrades that would improve reliability, reduce maintenance effort, modernize much of the 1920's technology to more modern standards. That there has been little to no significant improvement in run time should not be a surprise, as to do so would require megabucks more with each giving at best a few minutes and the most significant resultant of these changes would be improved reliability and elimination of maintenance headaches.
If you want to achieve significantly faster run times, I give you the following example: The Taiwan High Speed Railway. Taipei to Kaohsiung, 210.8 miles, all except the first few miles and the last couple miles on new alignment without speed restrictions between those points. Other than these end areas, the speed limit is 300 km/hr = 186 mph, without any intermediate points having speed restrictions. Most of these end area restrictions are in the 60 to 140 mph range, so they are not really that slow. The one stop express train does this 210 miles in 1 hour 35 minutes. The "local", which has six stops takes two hours flat. The station track layouts at these intermediate stations is such that there is no need to slow for the turnout to the station track. Simply do your braking like going directly into the platform and accelerating directly out of it. By the way, other than a slightly larger vertical difference, the platform offsets meet US ADA requirements.
Other than the end points, none of these stations are in the urban area they serve. Since the line opened in 2007, there has been considerable work done on transit connections between HSR stations and these urban areas. The total length of line is 214.2 miles end of track to end of track. Obviously, the track must extend beyound the terminal stations for some little distance for switching purposes. Of this all but the south about 2 miles are on concrete base track slabs, mostly the Japanese style precast segment type. 37.54 miles is in tunnel or cut and cover underground segments, with the longest two true tunnels being over 4 miles in length, each. 156.92 miles is on bridges and viaducts. Most of the south half of the route is elevated in its entirety, 97.75 miles of continuous structure. The remaining 59.17 miles of viaduct is spread over multiple structures, four of which are over 10 miles long.
Unless and until we find the money and space to build such a facility between New York and Washington DC, we are not going to get much reduction in run time below what we have now.
As to equipment, the Taiwan system uses a slightly modified Shinkansen 700 trainset of 12 cars. This means EMU, except that the end cars are unpowered. My viewpoint on NEC equipment is that we would have been far better off if we had taken lessons learned from the original Metroliner trainsets and built an improved EMU trainset rather than go with the European style end power cars and intervening coaches that we have now.