Is it OK to cover up soffit vents if they seem to be making rooms colder?

Don't block them. Those soffit vents are the intake side of your roof ventilation, and the air moving near the eaves is exactly what you want to see. Cold air comes in low at the soffits and exits high at the ridge or gable vents, and that flow keeps moisture from rotting your roof deck from underneath. Stuff them shut for one winter and you might barely notice a difference in the bedrooms, but you've quietly created a condensation problem you won't find untill spring.

The real issue is that cold air should be moving through that crawl space, but it shouldn't be moving into your house. In a setup like yours, the crawl space floor is basicly the ceiling of the unfinished space and the floor of your bedrooms. If that floor assembly isn't air sealed and well insulated, the moving air will find every gap around wiring holes, plumbing penetrations, and the top plates of the walls below. That's why the floors feel cold and why the baseboard heat can't keep up. You're not heating rooms, you're heating a leaky floor over an unconditioned space.

What I'd do is get back in there with a good light and check a couple things. First, see if there are baffles where the insulation meets the eaves. Those plastic or foam channels hold the insulation back and let the soffit air travel up along the underside of the roof instead of washing through the space. If insulation is just shoved against the vents, that's part of your problem. Second, look at the ceiling of that crawl space, meaning the underside of your bedroom floors. If the joist bays are open and you can see gaps, air sealing those is your biggest win. Caulk or foam every penetration, then make sure you've got a decent depth of insulation snug against that floor. Also worth checking the kneewalls if you have them, the short walls at the sides of the finished space. Those are notorious for being framed but never insulated properly in houses from that era. Blocking the vents treats the symptom and creates a worse problem. Seal the floor between the crawl space and the bedrooms instead, and those rooms will hold heat like the rest of the house.

This actually clears up alot for me. I have basically the same setup at my place, cold rooms over a skinny attic space, and I always assumed the drafty feeling near the edges meant the house was breathing wrong. Turns out it might be the air going where it's supposed to go, just leaking through the floor on the way.

I went up there last fall and saw some cardboard-looking pieces stapled between the rafters near the edge. Is that what those channel things are supposed to be, or is that a sign someone half-did it years ago? And can insulation sag or shift over 60 years, or does it basically stay put if it was done right?

One thing I'd add from my own place, which had a similar skinny space over the back bedrooms, is the access hatch. Mine was a plywood panel just dropped into the ceiling opening, no weatherstripping, and it was moving a shocking amount of warm air up into that cold space every time the furnace ran. I stuck some foam tape around the lip and put a weight on top of the panel and the rooms below got noticeably less cold without touching anything else. Easy to overlook because it looks fine from below. Also, if the rafters really are full of insulation in a vented attic like that, check wheather there's any air channel left above it, because packed rafter bays with no pathway can choke the flow even with the soffits wide open.

The tissue trick works great for finding where that air's actually going. On a windy day I hold a strip of tissue around anything I suspect in my knee wall space, and it'll dance like crazy right where there's a gap. Found a big one behind an old ceiling fixture that way, warm air getting sucked up into the cold space every time the heat ran. Also worth peeking at whether that skinny space connects to the main attic, cause if it does, the air's got a longer path than you think.