You're overthinking the problem and conflating a couple of issues. But that's okay because, as you said, this is a very solved problem with lots of great answers out there.

Let's break it down:


Tilemaps. Your first example is of a sprite walking across a bunch of tiles laid out horizontally (or sliding down a wall of tiles laid out vertically, they're isomorphic). One very elegant solution to this is to simply not check the edges of tiles where we know a sprite can't get to, such as edges that are "underground" or edges that border another completely solid tile.  

You're right that the sprite would descend due to to gravity, then move laterally, then get stuck... but the answer is to not care about the left or right edges of the tiles that are underground. That way, your collision resolution routine only moves the sprite vertically — and your sprite can go on its merry way.

Check out the Metanet tile tutorials for a step-by-step explanation of this. You say in your question that you're not using a traditional tilemap, but that's okay too: static tiles are in the tilemap and update as above, while moving platforms and such update as #2 below.
Other AABBs. You'll only run into a problem if, in a single frame, your sprite can move a distance larger than the width/height of most AABBs in your game. If it can't, you're golden: resolve the collisions one-by-one and it'll work just fine.

If the AABBs can move very fast in a single frame then you should "sweep" the movement when checking for collisions: chunk up the movement into tinier fractions and check for collisions at each step.


2D AABBs and resolving multiple collisions
Looking at the product page for Nikon lenses, I notice a distinction between telephoto lens and zoom lens.

What is the difference between the two?  Why would I want one over the other?  I wiki'd telephoto lens but remain confused about this distinction.

Please talk to me like I'm stupid. :) I am hoping for a completely lay explanation.  In particular, I'd like to understand in what situations I'd use a telephoto lens, and in what (other) situations I'd use a zoom lens.
