Gascoigne is pretty awesome, yeah. It wasn't supposed to be him, but it would be in the spirit of the game to leave it up to the reader to speculate. Personally, though, I think Gascoigne wasn't that close to the Healing Church (he was foreign, after all) and so would likely not have been tasked with such delicate things. Moreover, having daughters of his own, I doubt he'd have felt positive about the assignment.