In nnero's 1-2 IL he manages to find himself jumping at least 2 block high.
https:/​/​www.​speedrun.​com/​qbeh1/​run/​0y676x6m

After looking over it a few times, it seems that while jumping, ended up in the X,Y,Z of where his cube would be placed, despite knowing that the game's code would reject it, somehow still successfully placed the cube, got pushed backwards and up while jumping at the same time, thus leading to jumping 2 blocks high.

Have not been able to reproduce this glitch, nor have I seen it happen to anyone else, if it could be reproduced with any consistency, that would save a significant amount of time on in all categories.

Actually, I think I've figured it out already.
nnero's video was published on 22 May 2014.
Patch 1.0.1 came out on 23 May 2014, thus nnero was playing on 1.0.0 / 1.0.0 RC5.
If we look at the fixes we come to understand that version 1.0.0 / 1.0.0 RC5 had issues with players being able to place blocks while their model is inside to some degree.

Fix - "Ghost Cube is now more accurate with detecting the player"

That being said, if we can get access to 1.0.0 / 1.0.0 RC5 we'd be able to explore the uses of jumping 2 blocks high, but so far we can only go back to 1.0.3, hopefully we can find the other older versions soon.