Here's a few more options:
- Annoyance survival
- Counter cheese
All 3 are based on simply taking a heavier toll on their economy and time to let your ally tech up and kill them.
The requirement here is that you know they're double pooling.
1 Annoyance survival
scout the rush. as you see it coming, move 2 or 3 drones out of your base. Put one at the protoss player's natural, and the other 2 send to strategic spots around the map. Take care to avoid the lings as they're coming so he doesn't know what you've done.
Still try to salvage yourself by laying down a spine crawler and kiting with your drones, and every time they try to focus the spine crawler as it's building, cancel it and build another with a different drone, just delaying them. Your job here isn't to survive, it's to make them micro. if they are microing they're not focusing on their economy.
After they finally win and are taking down your hatchery, take one of your hidden drones and build a hatchery either at your ally's natural, or even in his base. Once all your buildings are destroyed they should realize what you've done. Now they either have to search the map for you (again distracting them) or ignore you and focus on your ally. If you didn't find a very strategic spot building in your ally's base is an option but a pretty crappy one. your income will be super slow obviously. His natural is a great place because he can help defend you when they come with their surviving lings, but it's the most obvious place to look for you.
Some random expansion spot on the map is nice but if they do send each of the 12 lings out and find you when the others arrive you'll have no help. But even if this happens, if you got 3 or more drones out of your base b4 they killed your main, then you can "hatchery hop" by laying down a hatchery, then as they arrive with the lings, build another one somewhere else and cancel that hatchery. This requires at least 600 minerals saved up, so this is probably only viable if you didn't even get your pool completed.
Another option is to see the double 6 pool coming and ONLy collect minerals and produce drones until they come, then run with your drones. Hopefully you'll have 600 minerals by this point and over a dozen drones to hide around the map.
The point is not for you to truly recover, but instead to take up their time and attention hunting you down while your ally goes to void ray.
2 Relocate (may not work because of build times)
Take 2 drones. if your ally's natural isn't adjacent to your main go there, if not then choose some other location.
Pool at 10 or so. then at 300 minerals lay down a hatchery with one of your 2 relocated drones. keep an eye on the rush with your scout drone. try to time it so that you are ready to abandon your main as he arrives.
Sometime around when he gets there, lay down a spine crawler at your new location. put it adjacent to your hatchery, and between it and the minerals. as his lings arrive, take all your drones and run out of your base. If you look like you're fleeing to your ally they shouldn't follow, but instead stay and finishe you off. if so just head to your new main. if not then try to kite and distract them as much as possible. While doing so, rebuild as much as possible at your new main. With some decent micro and luck you could easily have a single spine crawler, maybe 2 then run to your new main and use the drones to block off the spine crawlers and kill their lings or at least thin them out significantly.
I haven't tested it, but this may not be very viable because of the timing. you have to get the hatchery built and creep laid down b4 you can plop down that spine crawler. that all has to happen b4 they kill your pool. if they go after your hatchery first it should work. if they focus on your pool first then I seriously doubt it.
3 counter cheese
Pool at 10 or so. get 2 or 3 drones near their bases. as the rush comes, abandon your base and with the 2 or 3 hidden drones, try to sneak in a spine crawler or 3 near one of their mineral lines. if they're aren't paying enough attention you can get it laid down before they know what happened. even if they are, they'll have to hurt their economy even more to focus it with drones and at most 2 lings. if you lay down 3 all at once, they'll be hard pressed to get them all killed, and while they are trying, they won't be gathering minerals. giving your ally even more time to wall off and tech up.