Hokay, downloaded and installed, Win7 64-bit.
Not being critical, this is just what happened.
As soon as I tried to start the installation, I got a Win dialog, "Could Not Install," even though the install window came up. There's something in the install process that triggers the Windows response to reinstall with different parameters. I closed it, triggered your install process.
At end of install, error dialog "Couldn't register the hot key MOD_WIN:S." Also happened every time I changed desktops - I did not do any manual configuration, so the subsequent messages could have been prevented - but the initial message was not something I could prevent.
Desktop icon is pretty plain - the system tray icon looks much better

.
It started running immediately upon installation, but I didn't know that until I clicked the desktop icon. Not a problem, but a notification of some sort would be less confusing.
I'm running both Input Director and MS's Mouse without Borders - it's a test - and when I switched desktops, Input Director did not work
on that desktop, but Mouse without Borders did. Not a complaint, just information.
Don't really have time at the moment to check how things run on the different desktops, how to transfer running apps from one (1) desktop to another, and the like.
This appears to be a credible effort, and it seems to work well. All in all, I'd say congratulations are in order for a functional tool

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[Quick edit: 'twould be nice to be able to move a currently running app to a different desktop.]