Ok, solved it.

I found a program called Hot Keyboard ($29.95 for single license, 14 day free trial) that will let you do a lot of the same stuff as IntelliType, but also record and play keystroke macros.

First, I went into IntelliType and disabled Web/Home, Search and Mail keys.

Next, went into Synergy and programmed hotkeys for screen switches. CTRL-SHIFT-F1 for screen1, CTRL-SHIFT-y for screen2, CTRL-SHIFT-z for screen3 (I had wanted to do CTRL-SHIFT-F2 and F3 for the second and third screens, but for some reason when pressing those, Synergy registerd y and z - if anyone has an answer for that, it would be much appreciated).

Next went into Hot Keyboard. Chose "New Macro", named it, then pressed the key I wanted to use for firing the macro. First chose Web/Home, then for action type, chose "Record/Play Keystrokes". Set Play speed to Max (slider full right), then clicked on Record. Did the keystrokes, then clicked on the flashing icon in systray to stop recording. Repeated with the other two buttons.

Seems to be pretty much an instant switch - have yet to see how it works in game, though.