Why would the car stall if you open the throttle plate to let more air in, when the IAC is just a bypass valve to let air into the engine, which would pretty much act like a throttle plate...
Sounds like a sensor error with the MAF...
My brother had the same problem with his truck, Mazda B2500
Ran like [censored], touch gas alittle, it stalled, MAF was misreading what was going into the engine, unplugged the MAF, it ran like a dream
IAC is a [censored] on a Zetec, so I'd personally try to avoid it first, unplug MAF, car goes into Limp-mode, hopefully to where the car stays on, not where it tries to kill the car... my mom's escort won't run on Limp-mode without the MAF...