[Note: While I have heard some Story Time spoilers, nothing in this speculation comes from any of those spoilers. This is all pure speculation... the closest I have to any sort of "official" sourcing for any of this is one person on the subreddit who mentioned in passing that the Act I graphic novel "suggests" that TP/P is Hunter's father]
So I've been spending some time browsing some threads and re-thinking the story, and I saw somebody say on here (I don't remember exactly where) that the graphic novel might imply that TP/P is actually Hunter's father. At first I wasn't sure, but the more I think about this, the more sense it makes. The way I'm picturing it now is that Hunter is the son of TP/P and Ms. Terri, the Brother is the son of TP/P and a different ex-prostitute from The Dime, and "The Father" in Act III is referring to TP/P, not some other new character. Here are some of the things that led me to this:
- The beginning of the "Gloria" video clearly shows Ms. Terri sewing the tan armband. The Brother is shown to have a red armband. The two armbands are similar, but have important differences (e.g., different color, different tree design, stars, etc...). To me this suggests that the two armbands were made by the two mothers, and that they are similar women, but they are not identical. This also explains why Hunter would be drawn back to the other mother as a surrogate for Ms. Terri.
- There's a line in "Father" that says "I knew there was a reason I kept this". The conventional thinking seems to be that this was a reference to the poison bottle, but what if it's a reference to the red armband? The red armband is something unique to the Brother, and it serves as an identifying feature of The Brother in the Gloria video, so it would make perfect sense for Hunter to have kept it, as it would make it that much easier to steal the Brother's identity and to pass himself off as The Brother.
- TP/P is a Priest, so it's not that far fetched to think of him being referred to as "Father". (In fact, the "Congregation" explicitly refers to him as "Father" [... "won't you tend your flock and save us now?"]
- Other lines from "Father" include "And what of the Father, will he analyze?" and "Don't worry about The Father, you'll take care of him". Conventional wisdom is that this is Hunter hatching his plan to kill the Father, but what if it's just foreshadowing for what will happen? In Act IV, TP/P does in fact "analyze" and discovers Hunter's secret, but Hunter then "takes care of him" by making a deal with him (and then, presumably, by ultimately killing him). The latter line also says "YOU'LL" take care of him, rather than "I'LL" take care of him, suggesting to me that it's more of a foreshadowing of the future than it is Hunter planning something himself.
- There is nobody credited as "The Father" in the Gloria video. There's only The Brother and The General. It's entirely possible that The General is just a General, and is not related to either of them.
- This theory would necessarily redefine the way we think about HSHHAS, but imo, it still works well as being the reveal to Hunter where he finds out his mother was a prostitute. It would kind of be a stretch anyway if the meaning was "Hunter finds out his mother was a prostitute and had sex with lots of men; Hunter meets a man who had sex with him mother; Therefore the man is his father".