On mine it was relatively easy to workaround this problem as I let an AVR do the input switching so only have one input to the projector.
However, when first setting up my Harmony One I had told it to set the projector input properly, only to see it cycle through inputs and land on the wrong one quite consistently. What a PITA. Since my AVR does all the switching anyway, I just told the Harmony (via the setup) that the projector stays on the last used input, so it doesn't try to change it as part of my activity.
That said, if you need the harmony to set your projector to a specific input in a reliable way, a possible fix is to have your Harmony remote duplicate the "Function" button from your projector remote. The "Function" button is a customizable button that can be assigned a task to through the projector OSD menus. I noticed last night that you can set the function button to jump to a specific input. So set this up (say, assign the function button to HDMI 3) and then have the Harmony execute this as part of your activity sequence. To my knowledge this function button is the only way to get the projector to switch to a specific input directly.
This of course may only be half the battle for you as this is 'one way' switching. Otherwise all I can suggest is buying an AVR.