The game can be solved by methodically boxing in your character with normal crates and warping upwards, preparing a new box every time and warping as you ascend.
The only deaths you will suffer from this point on come from glitches(that need to be fixed). Namely:
Some of the melee enemies can spawn INSIDE of crates and advance towards you, killing you.
Scraping against pre-stacked boxes that are closer together than the height of the character's hitbox instantly kills you for no apparent reason (presumably, the game is acting under the assumption that one of them is following you)
I'm assuming that the piercing-laser firing enemies were designed to mitigate the effectiveness of this strategy, but it's possible to work around them.