It seems to me the idea of gathering in, whether fast or slow, is much different from gleaning, as the latter really refers to taking up a small amount of leftovers.

But do they gather up the small amounts of leftover hay, and make the leftovers themselves into bales? Because that's the use of gleaning (for information) that I use; you kind of put small hints together and conclude something which wasn't told to you outright. As in, your girl friend keeps referring to her boyfriend in the past tense, and when she says "By the way, we broke up, you know" you say "So I gathered." You gleaned that from her hints!