Unless I've missed something, this is a possible endgame, even if our card draws do not improve (quantities in red are cards remaining in Player Card draw pile, which currently has 18 cards left):
Jimm takes 3 red cards from me (using 3 actions) and cures red with his final action 16 left
SFS drives to Toronto, autotreats all blue, drives to Chicago, autotreats all blue. 14 left
Schneau flies to Madrid, drives to Algiers, drives to Cairo, treats one cube. 12 left
Shraeye drives to Shanghai (treating for free en passant), to Hong Kong, to Kolkata, to Delhi.10 left
Jim flies to Khartoum (discarding Khartoum), treats, drives to Jo'berg, treats. 8 left
SFS autotreats yellow, drives to Atlanta, autotreats blue, has action left. 6 left
Schneau drives to Baghdad, drives to Karachi, drives to Delhi, and builds a Research Station 4 left
Shraeye shares knowledge by taking the Delhi card from Schneau, and cures black. We win immediately upon 4th cure - Shraeye need not draw cards.
Now, I haven't considered all the data (top of infection deck, or where we are on upcoming epidemics), I just wanted to get this down. But I think this may work regardless, and here's why. We currently have no 3-cube cities. And only a handful of 2-cube cities, most of which I've covered with the moves above. The current 2-cube cities that don't get treated under the above plan are Riyadh and Sao Paulo, so that needs to be looked at, but the cities around them will not chain, and we can afford a single additional outbreak. Plus, we should be getting some special event cards that will help even more. Thoughts?