I never went for jobs-as-storyline with Blades, and I don’t think my players were too interested in that. Instead, our “season arc” came out of playing out their downtime instead of skimming past it. Downtime is all about what the characters want/like/are addicted to anyway, so it’s much more personal than the crime stuff. That gave us plenty of NPCs making emotional demands, ammo for putting the PCs at odds with one another, etc.

I don’t know how much work you’re putting their contacts or backstories or whatever on display with NPCs as opposed to just the big Factions, so this probably isn’t news to you — but it worked pretty well for my game.