While this may not fit in with the theme for Noxico, and may be just a personal preference, What if the '2 lives before permadeath' mechanic was replaced with something along the lines of the games 'Halls of Degeneration' or 'Flexible Survival', where being defeated by another enemy will add a transformation to the player of the type of the enemy. too many loses will result in a game over.
This method (speaking closer to Halls of Degeneration), will still make losing dangerous due to the player not respawning at their home, and must still fight the enemies after being defeated. in Halls of Degeneration, when a player loses, a dialog appears that explains the type of transformation, and gives the player about half their hp back, before they can move again to flee or continue the combat.