Defeat multiple insane AI opponents with Zerg

Solution 1:

Both Terrans and Protoss can build harvesters and units simultaneously while a Zerg can't.

— Sorean's comment

What he says isn't 100% true, you can produce queens for (early) defense while producing Drones.

Which brings you to a Spanishiwa style way of playing Zerg, where you should root your strategy.

The general idea I have on this:

• Do not create Extractors very early until the point you come to upgrading your base.

  Why? You don't need gas so early on.

• Focus on getting a queen out and spread creep till the ramp; keep producing queens as defense!

  Why? Creep is needed for crawlers and to serve as a speed bonus for your slow queen army...

• Get Spine Crawlers near the ramp and add Spore Crawlers to the mix later on.

• Get a second Hatchery in base, this allows you double the amount of Larva and queens you get.

  Why? This kind of exploits the 4OC style of playing, so you produce double as fast. :)

• Get out for an expansion; don't forget your extractors and upgrading your base.

  Why? Because you come to a point where you just can't hold it on your base alone...

• Mass up a Brood-Lord army with some defensive Corruptors or whatever unit composition rocks...

The effectiveness of this depends on your execution of a Spanishiwa style build order, see for yourself if it's impossible for you at this moment of time. I bet it's possible when one does a lot of practice...