We're almost certainly doomed, but we still have a smidgen of a chance. If Agnes and I each can seal one red Gate, we can survive the Mythos phase if we're lucky. This means nobody goes to London, so our only chance is if the next Mythos card is green (50% chance, as two cards remain and one of them is green). Then the Clue spawns, and there will be no Reckoning to destroy it. In Turn 14, we'll need to make sure we get that Clue to solve the third Mystery. When the final (yellow) Mythos card comes up, the Omen will advance to blue, which is safe as long as no blue Gate opens (and a green card won't spawn a Gate; the monster surge will happen on the only remaining red Gate, matching the Omen). Then we'll have one last turn to confront the Black Pharaoh and get two Clues on the final Mystery to win the game.
If Agnes goes to Space 10 with her free move, she can then use the Shining Trapezohedron to get the Fire Vampire out of the way before moving on to Rome. Then I'll Travel to the Sahara Desert, using my free move to go to Alexandria first. With my other Action I can go shopping in Alexandria. That Book of Spells may prove useful. Alternatively, I can get a second Focus or Rest and try to use the Canopic Jar. Or, if I go before Agnes, I can Trade with her.
I probably shouldn't be Lead Investigator. Depending on where the Clue pops up (if it does), I may be the only one who can reach it in one turn (with the Livre d'Ivon).