When you finish the game I think there is a way to replay the mission on "hard mode".
But on your proposal: you still already play out the card before slotting it, and it will worsen the effect of "some" of the damage...not all, so I am not sure increasing the way some damage stick is the way to go.
Maybe getting damage from the minions attacking also diagonal in your back? (so going from 4 max damage to 6), and it will make "facing" matters.
Then increase it to a max of 8 (all spaces around the mech) for "nightmare" difficulty
I wonder if it will work to allow subsequent damage to happen after the resolving all the initial damages to increase the difficulty? (i.e. when all the damage cards are resolved, if the mech lands next to new minions, it will get additional damage (using the original rule of adjacency (max 4)). It might throw an additional monkey wrench into completing your objective and schematic card like barrel roll might not help as much.