It's all about the way that the tv inputs are selected from the remote.
Suggestion 1.
Set the input that the tv always starts at to AV2, then it should not nees to shuffle through the others.
a. Click More Options on your Harmony home page for the tv.
b. Click Change the Setup of this Device. Follow the online instructions until you get the page with the heading "When you turn your device off and then back on again, does it go to a particular input or stay on whatever it was on when you turned it off?"
c. Select the appropriate answer from the drop-down list and click Select.
d. Click Skip if you are prompted to reconfigure any activities. NOTE: You may have to click Skip several times depending on how many activities are in your configuration.
Suggestion 2.
Set up the tv and harmony so that each input can be accessed by a single keypress. On some tv's it is possible to set the source for a channel on the programme list e.g. 1 to 5 have analogue frequencies but set '7' so that it does not go to an analogue frequency, but goes to AV2. If you can do this, do it for all your inputs then set up the harmony to use them to directly access the inputs from separate buttons, e.g. 6 activates AV1, 7 activates AV2, 8 activates AV3 etc.