I think you're dead on with the idea of Jack as Philoctetes. I don't think it was unintentional, either, how the two 'aliens' tell the story. Mary twists it to fit her own experience, and Jack applies his worldview to it, which I'm thinking owes a lot to his Time Agency days and what bits he's caught here and there, cause he knows a lot but it comes more from experience, he's not really a scholar. It makes sense to me that he'd synthesise the story to what it really comes down to (even though it's a lot more than that), because he's a pragmatic kind of guy and also, he loves going for the punchline, he'll make anything funny if he can.

And of course now that you mention it, Tosh reminds me a lot of Faust in that episode.