After much struggle...
I can do transit multitasking
Okay — I think the Live Activities for Railtime might actually work. And you'll see what all of it was for. All so I could see this on my lock screen (and do other stuff on my phone while still being able to see the train).


It's toggled on not via a set alert time anymore (which proved sort of useless, as you still needed to open the app to start the Live Activity), so that's gone from Settings. Instead, it's done manually, and... for the exact trip you desire. On the Station Detail view, you long press a trip and you're greeted with a few options:

I think "Live Activity" explains it well enough. As soon as you start it, the Live Activity kicks in. And it isn't for the next trip on the route: it's for the one you choose. So at 4:21 p.m., I can spy a lovely B train heading south at 4:37 p.m. and see on my lock screen exactly how long it'll take for me to barely miss it.
You might notice something else there, by the way. Yesterday I was thinking, "It'd be really cool if you could get an arrow that pointed you to the nearest entrance for a route." As it happens, the MTA provides coordinates for the entrances. So you tap "Find Entrance," and...

Well. I messed the continuity up. Long press on a W trip and then took a screenshot of an R trip. Oh well. Also, it looks like I'll be walking awhile to get to the closest entrance for Times Square-42nd St.
Minor thing, but two screenshots up, rather than every trip being labeled as "North" and "South" only, they now feature the final destination (last terminal) for the trip because, really, I should have been doing that from the get-go.
It could be prettier
Now that the bones are mostly set, I've been thinking about how I could make it look nicer. As usual, an idea popped into my head and refused to leave, and now I want to do it.
For each Station Detail view, I want the background to be a photograph of that particular station.
Naturally, I first looked at several online hubs for royalty-free images to see if it could be accomplished that way, and, yeah: aside from the more well-known stations, there are not many free and usable photographs to be had.
There are, functionally, 423 different places you can hop on a subway train in New York City. Because I cannot say no to myself, I will attempt to snap a pic from every single one of them.
I'll at least try to be smart about it: maybe see if I can do a Shortcut that ropes in the locations, select the location, take the photo and dump the result to a folder with the image named for the station ID. Feed the images to Railtime, tell it to match the image to the station ID, done.
This is going to take a while, though.