I really like Fate Accelerated for CONs, because it's flexible, people get it once the FATE dice are rolling and young folks -especially teens- tend to run with it. I've mostly run and played it at CONs as 1-shots, but I can envision it working for 3 episodic, linked sessions. Speaking of post apocalypse, one of the best FAE games I played in was where the Host subbed out the standard 6 FAE approaches with the SPECIAL (Strength, Perception, Endurance, Charisma, Intelligence, Agility & Luck) from Fallout. It ran really well and I was surprised with some of the creative things my son and other teens came up with. Lots of fun!
Were I to run a PA game at a CON this spring it'd probably be Fallout themed, because the franchise is getting a lot of exposure this year. There's also the 2d20 Fallout which is a nice, lighter implementation of those rules. It might work better at a CON for 3 linked episodes, due to having more play mechanics/options baked in. Your players could even adavance if you set a short milestone.