Home theater isn't a device mode, it is a redirection to the other device modes. I think the PIP group defaults to TV unless you changed it. To map the MOVE key in HT "mode" you must map it in the mode (default TV) that the HT PIP group redirects to.

I think you confused the call center to get the answer you quoted.

To use set as a shift key you press it before the key you want shifted. You do that both during the 994 command when you define a meaning for the shifted key and each time you want to use the shifted key.