All of season 7, and missions 1 and 2 of season 8 are on DrivethruRPG ... but that only helps so much.
But there is a sort of back-door approach. "Chicago Chaos" is a book that was put out for the ShadowRun Anarchy rules set. Has a bunch of Anarchy goodies, but more importantly for you it has capsule outlines for a campaign in Chicago ... which is basically the Chicago missions. Slightly altered and much abbreviated (average less than a page each, no details on nuyen or SR stats for foes, no maps, etc, etc). I'd much rather have the actual missions, but I managed to complete the story arc using what is in Chicago Chaos.
Also seasons 7 and 8 have much more of a story arc to them, each ending with pretty dramatic finales.