On top of using the engineer, forests can also help. If your capital has some, may be keep a few forest tiles until you're about to get Itza. Then work 'em forests, best if your workers would finish cutting some forests 1 turn after you started to build Itza. If one of your other cities have lots of forests, may be send several workers there in advance and cut like mad, perhaps it'd be even faster (with an engineer or even without) than to build it in the capital without any forests. Given few turns needed to cut forests, may be 2nd round of cutting 'em could also be done before some AI build Itza.
I had mightily great time cutting forests for a wonder - in my case, it was a great lighthouse i was willing to build ahead of an AI, and it worked awesome. Without cutting forests, i'd be having less than half of the great lighthouse built before AI would finish it. 5 or 6 forest tiles cut (don't remember precisely), and i was well ahead of an AI finishing the thing.