This could all be plausible but the way you describe it all happening makes me think it's not the battery that's the issue.

Check the metal on the battery terminal hookups. Not the ones that go on the battery but the metal that extends out from it if it feels very weak then your problem is probably that they are corroded. I have no idea what metal they are made of but these do corrode without that much noticeable wear. I had to replace mine and another person I know had to do the same.

For us, it aounded pretty close to what you have with the exception that if you wiggles the battery cables enough, it would cause a connection good enough to start right up. But sometimes the battery would just go dead. This was due to just enough of a connection to start the car and of course the alternator would take over at that point but then the battery still had to power some things and wasn't getting good enough connection from the alternator to charge.

Hope you figure it out!

There's always the possibility of parasytic draw as well..