Thanks David, that is helpful, it certainly cuts down the complexity quite a bit. 
But I still would like to be able to get this down to one click, and I have programmable buttons left on my harmony remote. 
I also discovered that just pressing channel buttons on the remote - EyeTV won't change tuners, it will only do it if I bring up Menu, then Channels and then select one there, which is still a bit cumbersome (but certainly better than Menu, More, Inputs, then selecting an input!)

 
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