When my brother and I took a rail tour, with two exceptions – from Sunset to Southwest Chief in Los Angeles with connection of eleven hours and Capitol to Philly with the NEC connection to DC running like busses – we would overnight, specifically Chicago, Pittsburgh, and New Orleans.
The Chicago connection would have been really tight. Pittsburgh we would have been okay despite the 90-minute connection but neither of had been there and we were two nights in the city anyway. NOLA was also two nights because the Sunset left before the Crescent arrived and Sunset is a tri-weekly train, not daily. That was also okay because my brother had never been in New Orleans before and loved it.
Another layover was detraining at Altoona and staying three nights at a railfan-oriented B&B in Cresson. My brother and nephew, who joined us there from DC, got thorough lessons in rail lore.
Yeah, this was my first time having an actual connection on Amtrak, and honestly I was worried about it from the moment I booked it. But I read on Reddit or something that they will often hold the train for connecting passengers, so I decided to risk it. It turns out I gambled and lost – in this case we were so late they couldn’t hold the train bus that long. What I should have done was what @DesertDog mentioned, and booked my train to arrive in Portland a day early and given myself a ~25 hour layover.
When I took the Zephyr to Chicago a few years ago we were similarly late, but I didn’t mind that much because I didn’t have a connection to make or any big plans when I arrived in Chicago.
This was at least partly because we had pretty much an express bus between Portland and Spokane. They had two buses, and they put everyone who was traveling all the way to Spokane on one bus, and the people who were going to an intermediate stop on the other bus. Our bus went directly to Spokane without stopping (apart from a brief stop at a rest area). The other bus stopped at all the stations the train would have stopped at. I’m told that bus took an hour longer. They did the same thing for the return trip to Portland.