I'd usually run a larger squad of Spiders then that, but what you have should work OK.
I'd drop the spirit stones on the Falcon, and pick up powered blades on your spider exarch. That gives you an additional 4 power weapon attacks on the charge, considering they are only striking at s3, the difference between 6 attacks and 10 is significant. Also keep in mind that the Autarch (because of s3 again) is not a particularly fearsome opponent. Be very careful you don't bite off more then you can chew! Warp Spiders have excellent mobility so make sure you are engaging targets that you can beat. Namely use them to shoot then tie up backfield fire support units- like long fangs and loota boyz. Withdraw is great for bouncing from squad to squad. Just be very warey of real combat units!!
I really hope you are right about not needing av14... if your autarch fails to stop a land raider- then it will literally walk all over you.
Other then that, it looks like a pretty fun list. Ninja Autarch + Spiders is good times. Good luck