Here is what helped me, but so much of this just comes down to having the right tools at the right time.
Expatriette: in your opening hand, look forHair Trigger Reflexes. Aimed HTR is the single best protection the team has against thieves and informants, so getting that out immediately is incredibly useful. Hopefully you get some Cryo ammo later, for when the chairman flips
Fixer: having a jack handle to start is amazing. The ideal is to start with the handle, get out mantis style, then switch to crowbars once the Chairman comes out.
Nightmist: starting with a mistform is amazing. It helps absorb so much damage. Oblivions are just as good, unless the contract is out. I really like using her base power to arrange it so that a heedless lash will play a necklace or stabulet.
In the later game, an Astral Premonition can help you control the deck
rook city: hope that you get tremata and Tony out ASAP, and try like hell to survive. There's no good strategy here that I've found.
The Organization:
so much depends on what comes out when.
In general, you need: Prison Break to be played ASAP (preferably first turn), then the second one to be played either immediately thereafter, or uselessly.
It really, really helps if the first thing out is the broker- you can accelerate the deck and try to kill everything except the underbosses right before the shuffle (Jack handle/bloody knuckles/grease monkey, with most form works well for that). Alternatively, if you have an early oblivion and the crowbars, go hyper aggressive ASAP and try to get the chairman to flip ASAP... Though you still really need those prison breaks to come at the right (for you) time.
be SHAMELESS about using the rewind. Oblivion fizzles because of revealing dual 1's? Rewind. Did you forget retaliation damage and end up dead? Rewind! Did a prison break come out and undo everything? Rewind!
in the end, it is all about luck and getting things to align. I'll readily admit ragequitting when the contract was the first out and expat started with no guns. Or just plain restarting again and again until the heroes started with a loadout I thought might work.
Good luck! I hope you get it.