I wasn't alive during their heyday, either. But I've collected a lot of literature from the period, mostly back issues of the Official Guide of the Railways.
The 20th Century did make stops for servicing and crew changes, but there were no passenger stops between Albany and Englewood (at least for most of its history). The New York Central, however, did operate a number of other trains which were targeted at specific markets, such as New York to Cleveland. So the cities and towns in "flyover country" were well served, and at much more convenient hours than you find today.
Since you seem to have put a lot of effort into this, do you mind if I ask some follow-up questions?
Were all those trains run on steam engines when they had their best timings? Or did any of the routes use diesel or electric locomotives?
Where were the service stops for 20th Century between Albany and Chicago?
The best timings, almost universally, would have been in the Diesel era...but before the ICC's 1947 edict restricting speeds to 79 mph or less on track not equipped with cab signals or Automatic Train Stop took effect in (IIRC) 1955. Diesel locomotives don't need water stops (or track pans....) which steam locomotives need every 50-80 miles, and they can generally go farther on a tank of fuel than steamers can go on a load of coal.
I don't know exactly where the Century's service stops were; perhaps a New York Central fan can chime in.
I'm the resident Central fan here so I can comment to this. The train stopped for an engine change at Harmon, then Albany, Buffalo, Cleveland, Toledo, Elkhart/South Bend. For the longest time there was no stop between Harmon and Englewood to my knowledge.
Steam locomotives it really depends on the engine to what its coal and water consumption. Also what you are hauling and at what speed. In twenty car excursion service we have pushed 611 (northern) 295 miles without coaling and taking water. But we also have the use of an auxiliary water tender and are restricted to 45.
I can't speak for the J3A Hudson because none were preserved but likely you could get a good 150 between coal and with water pans probably wouldn't need to worry too much about that either. I know some trains back in the day used to change engine every so many miles. The Hudsons weren't all they were cracked up to be.
They were great engines for power at high speed but getting started they were horrible. They were even fitted with one diesel traction motor to help get them to speed. The Niagara's were far superior engines.
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Amtrak Routes I've riden: Silver Star(NYP-ORL), Silver Meteor(KIS-NYP),Carolinian(CLT-NWK), Palmetto (FLO-NYP), Acela(WAS-NYP), NE Regional(WBG-RVR), Pacific Surfliner(SAN-OSD), Piedmont(CLT-SAL), Crescent(NYP-CLT), Cardinal (WAS-CHI), Capitol Limited (CHI-WAS), Cascade (PDX-SEA)
Steam Engines I've worked behind: Norfolk & Western No. 611; Nickel Plate Road No. 765; Southern Pacific No. 4449