Seems interesting, but the mechanic is unclear in a way where I can't tell what's me not understanding the mechanic or what's a bug. For example, in Configuration 4, by spamming the X key while pushing a box to the west, I managed to simultaneously make a box I can't push with an invisible box to its immediate east.
EDIT: Ok, I get the intent now. Lbh pna mnc n pengr gb terrayl gvzryvar rirag gung jvyy fcnja n pengr ng gung ghea. (Hayrff lbh'er ba gbc bs vg jura vg gevrf gb fcnja, gura vg whfg qbrfa'g.) Gurer vf ab terra haqb ohggba, bayl tenl haqb, ohg erfgneg vf n gehr erfgneg.
EDIT 2: and also, N pengr bs ntr A perngrf n pengr bs ntr A+1 jura qhcyvpngrq. Vs vgf pengr bs ntr A+1 nyernql rkvfgrq, vg qvfnccrnef (rireljurer nyy ng bapr, V guvax). Gur znkvzhz ntr vf A+3 naq ng gung cbvag lbh pna'g qhcyvpngr vg nalzber.
What you describe in Configuration 4 does appear to be a bug sorry, I have managed to reproduce it but can't really upload a fix until the jam rating period is over now.
From what I can tell it occurs if movement and displacement occur on the same frame, which can be caused by spamming inputs.
The explaination's in the edits are pretty much correct, although that's not how I really conceptualise the first point when thinking about it personally.
I will probably write up a postmortem at some point explaining the mechanic and its inspirations in a bit more depth.
Thanks for the feedback!