Okay, so that pretty much leaves the receiver and barrel. Have you looked in their with a flashlight to see if the extractor relief cut in the barrel face is clean? It could have something in it, even dried cosmoline, that's just not letting the extractor move enough to snap over the rim. The cartridge doesn't have to fit into the bolt face before it's chambered. A properly functioning Mosin will close the bolt on a cartridge even if it's dropped in the chamber first.
Just to be sure that it isn't the bolt, try that bolt in another Mosin also.
BTW, you should be using dummy cartridges for this unless you're at the range and pointed at the berm. Be careful.
Will a cartridge drop fully into the chamber? It's rare, but I've heard of people buying guns that had a cartridge case with the head torn off still in the chamber. If so, you just need a broken case extractor, and maybe some cleaning if it's a steel case and it started to rust. I know you said you looked in there with a light, but it can be very hard to see something like that because of the shape of the chamber.