Get some sort of Virtual Network Computing app for your phone. I use iTeleport. With it you can control your computer from your phone so you can hit the super lucky button or watch sbtv as long as your computer is on and connected to the internet.
Be warned though, because a lot of VNC apps are expensive (iTeleport is 25$ I believe), but I think there are a few free ones.
If anyone finds the above information useful and hasn't signed up for one of these sites yet, here's my Superpoints link, and here's a tutorial I wrote for Swagbucks.
Try this: http://www.iteleportmobile.com
I've used it for years when I first got an iPhone with several Windows PC's and in the 2 years I've had a MacBook Pro I've used it more on the laptop to remote into my personal machines as well as several Mac Mini's for work. I like it, it replaced Log Me In personally and professionally for my uses.
>but currently my only option is to remote-desktop into the machine on my desk; which is many ways is a worse experience because iOS/Android touch inputs are translated into mouseclicks by the RDP application, not to mention the inherrent delay
On iOS you might want to check out iTeleport ( http://www.iteleportmobile.com/features ) It has the option of making the iPad display effectively a huge trackpad. It works surprisingly well for controlling an RDP session.