Turns out... something was locking my file. Once I figured out what it was, this turned out to have nothing to do with Felix. Anyone who has a similar issue should not believe in the least (as I tended to, since I'm new to OSGi) that the lock on the file was at all related to or a part of the OSGi framework. It wasn't here and almost certainly won't be, even for other frameworks; as I've researched, that would be a major departure from OSGi to begin with.
Anyway, my issue was solved by figuring out what component of the bundle wasn't getting shutdown before I tried to delete the JAR that was being held open because I had inadvertently told it to remain open. GI,GO.