Motorized roll curtains with Wi-Fi control

So I've been thinking about making motorized roll curtains (blackout curtains), using stepper motors and controlled by a remote. This is mechanically exactly what I want to do: YouTube link,

I have a Logitech Harmony Smart Control universal remote at home to control my AV receiver, HTPC and TV, I would love to be able to trigger the curtains with it too. But the remote doesn't send out RF signals, so getting a 433mhz module is ruled out. So I would prefer to do it via Wi-Fi but most all Wi-Fi control arduino things I've seen are web browser controlled, I dont know if this would be controllable via the Logitech remote? Has anyone got any experience with Arduino Wi-Fi control with a Logitech remote to share?

In total what I gather I will need is 4 stepper motors for the windows I have, an Arduino Uno (possibly with the WiFi module integrated), a CNC 4-axis motor shield to control the motors and stepper motor drivers for the shied, something like this: eBay link.

Any thoughts, comments or suggestions? Am I headed in the right direction with this, or should I go for IR instead, or even a physical button to press? It would be great to get it to work with my Logitech remote if feasible.