QuietCool Whole House Fan 4700 and a relay

It could work but not by itself. It is designed to be used in lighting applications so the 1600w is going to be resistive max. Here is warning given in the amazon description:

Designed to work with regular light switch. THIS IS NOT MOTOR CONTROLLER. Ceiling fans and other motors require DIFFERENT device to control . Incorrect device usage void the warranty. Returning it as defective in this case is Amazon return policy violation and may affect your buyer account.

So you would need to add relays rated to handle the fan which would be an option.

Or use two high amp rated z-wave relays one for high speed and one for low like
http://www.zwaveproducts.com/shop/controllers/contact-modules-and-repeaters/15-amp-dry-contact-module

http://www.zwaveproducts.com/shop/controllers/contact-modules-and-repeaters/z-wave-relay-fixture-module

Maybe the way I did my high-low speed control for an evap cooler could help. Look at the wiring diagram at the bottom, it might give you some other ideas… [OBSOLETE] Evap Cooler Thermostat