Unfortunately, there is not a way to do this in MediaShout at this time. It would be like you said: adding the text box to the left side to leave the right side open for the PiP. Or, just make sure your text box does not go down too far where it would be covered up by the PiP.
I do see your reasoning and frustration with this. I'll pass it along to see if we can do something to make this process easier for you.