Your theory at least has merit. And you're doing what Q admonishes: Think logically! This is important!
All the same, and no offense, I still think that Q is Eric Cartman (aka EriQ Qartman):
Haha! But is Cartman heavily invested in John Perry Barlow? Bannon is, which would explain Q’s bizarre fixation on Barlow’s death.
There’s more, but the Barlow stuff always stood out to me as a good, albeit strange, indicator.