The new one, Little Red Riding Hood. This was the other way around, compared to recent comments here: easier to put back together than to get apart. The reason: Screws holding on the bottom plate not only all around the edge, but also a few from above -- hidden under the keyboard. So the keyboard had to be removed first, and this in turn was a twothree-step operation: First a couple of screws from below, not along the edge but in the center of the bottom plate had to be removed; then the keyboard needed to be pushed up from below, using a match or similar (I used a toothpick, snipped off to be blunt at the ends) through these screw holes, so the edge came partly free; only then could the rest of the edge be pried out from under the edge in the top housing that holds it in place... And finally the KB could be flipped aside to get access to two or three the screws underneath that hold the bottom plate from above.

After that, getting the bottom plate off was easy-peasy, and the bit that had been rattling around inside came falling out almost before I'd opened her up. Turned out not to be a screw that had fallen out from holding down something on the inside, as I had suspected, but one of the "teeth" around the edge of the bottom plate itself that are there to guide its edge into place when closing it. Annoyingly, I had probably broken that off myself: A few days earlier, I had noticed that one corner of the bottom plate flexed, was no longer firmly attached to the frame. I deduced that the screw that holds that corner had loosened, and resolved to screw it back in. Had I done that immediately, that would probably have been the end of it. But for some reason[1] I didn't, and then, like how you compulsively poke at a broken tooth with your tongue, I kept pinching the frame and bottom plate together several times during the evening (or possibly two). This must have been what broke off the minuscule piece of plastic.

https://photos.app.goo.gl/FPbo8UknGRGdgojn6

So, a bit of an anti-climax: I never got around to do any of the sleuthing for the origin of my supposed loosened screw that I'd been looking forward to. But, OTOH, relief: No parts dangling half-loose, and I got to close her up without poking around inside and possibly wreaking more havoc than doing good. All in all, encouraging: Won't be so scared of doing it another time.