How to calculate the probabilities for eliminative dice pools (dice cancelling mechanic) in Neon City Overdrive?

The game Neon City Overdrive uses the following resolution mechanic for checks:

  1. create a pool of Action Dice and (possibly) another pool of differently-colored Danger Dice (all d6, generally up to 5 or 6 dice in each pool)
  2. roll all the dice
  3. each Danger Die cancels out an Action Die with the same value – both are discarded
  4. the highest remaining Action Die (if there is any) is the result (the precise meaning of which is irrelevant for the purposes of this question)
    • any extra Action Dice showing 6 (i.e. in addition to the single highest die read as the result) provide a critical success (called a boon)

I’m struggling to find the proper way to model the probabilities of this mechanic in anydice.

I realize that a good starting point would be this answer to a very similar question regarding the mechanic in Technoir (which clearly was a source of inspiration for Neon City Overdrive). Unfortunately, despite my best efforts I can’t say I fully comprehend how the code provided there works, and there’s an important difference between the two games: in Technoir a single "negative die" eliminates all matching "positive dice", whereas in NCO this happens on a one-to-one basis.

I would be very grateful for any help.