Have you ever seen the TV show Chopped? The idea is simple. Four chefs are given a baskets of weird mystery ingredients and forced to cook a three-course meal using and featuring the ingredients in the baskets.
I was thinking that might be the basis for a fun Netrunner event. At the start of the event, players are given 3 or 4 cards that they have to use in building decks. The cards should not be traditional power cards, should be from various factions, should be fairly low influence cost (so they don't force everyone to go the same direction with them), and should be not obviously synergistic with each other. Players are then given a period of time to brew two decks using the mandatory ingredients. To keep with the Spirit of the game, they should be required to use the mystery ingredients as a 3x card.
They can then play some games to win points. You could add on an aesthetic element and have some judges rule on their decks and the degree to which the decks were built and played to actually feature the mystery ingredients. If the players put the cards in but basically just discarded them all the time, they could be penalized or just publicly shamed.
It might be a bit complicated to pull off easily, but it might be fun and it would feature both the deck building and deck playing aspects of the game. Just a thought.