League-of-legends – How are champion displacement moves prioritized

There is a hotkey H which is the equivalent of toggling "Stop", which stops your current action. I'm not sure whether this will do what you need in stopping the auto-attack, but it's worth a try. I don't see any other options that could remotely do what you desire, other than getting stunned.

Continually pacing back and forth within range is a preferable course of action once you learn how to do it without getting exhausted. This actually has a few benefits besides just preventing you from attacking - it makes you a harder target, and it also makes it less detectable to be seen creeping closer and closer towards your opponent to make a pot shot. Alternatively, it makes your opponent uneasy since you can easily be in range to take said shot, which makes them less inclined to stay close.

[..] a bigger Champion means a bigger target to aim for by enemy skillshots.

This is correct, but isn't necessarily a disadvantage. Most of the characters with large+ hitboxes have more hp, armor, magic resist, etc and are better suited for taking damage. With a larger hitbox, it's easier to intercept skillshots and other abilities to protect squishier allies.

Also, characters with large hitboxes can stand on "top" of other champions, making them harder to target.

Other than this, I can't think of any direct advantage provided by a larger hitbox. Spells that increase the hitbox often directly affect the champions stats (think of how Cho'Gath gains HP with each feast), but the size increase itself does nothing.