Very good article. Unfortunately I'm not good enough in english language to express the problem with the encounter as well as you.
A few other remarks:
1/ Answering the first question requires a DC 25 (or 35) Knowledge check. According to the rules, DC 20 to 30 is for "really tough questions" and DC 35 knowledge check doesn't even exist. I'm not arguing if level 15 PCs should auto-succeed a DC 25 Religion check (spoiler: they shouldn't. A cleric can have ~+18 in Religion, ~1/3 of failure), I'm saying she's asking an obscure trivia like "Conventry City last won the FA cup in what year ?", and she hit PCs with lethal damages if they can't answer. That's not just unlawful and ungood, that's also stupid for any reasonable measure of "stupid". So stupid even a Chaotic Lolrandom god wouldn't do that.
2/ One of the "official" justification was that god in golarion aren't perfect, so they may lose their temper. But Iomedae isn't just "not perfect", she has act like a 5-year-old kid. In all seriousness, you could replace Iomedae by Cartman and the scene would work the same: Cartman abducts the PC, then he convinces himself it's an honor he's doing, and if they say something he doesn't like he shout "respect my authority" for sonic damages.
... OK, Golarion gods aren't perfect. But at least, the LG parangon could
try to be perfect. Here she isn't even trying.
3/ Asmodeus is the god of fantasy nazis, so I imagine him beating the shit out of people until they say what he wants to hear. As opposed to Iomedae, who... beats the shit out of people until they say what she wants to hear? Thanks to this encounter, I can't tell the difference between the LG parangon and the LE parangon. The color of the lasers?
4/ The encounter could have been cool
and consistent
and dangerous. Until that point Paizo didn't write any rule about gods, so authors could have decided gods are so powerful, their mere presence hurts the PCs; and Iomedae is making conscious efforts to hold her power. Efforts detectable by an easy Perception or Psychology check (two skills usually much higher than Religion among players - at level 15, a DC 20 or even 25 check should be an auto-success for someone in the party). Each time she lose hes temper or her patience, she involuntary hurt the PCs - then she apologizes, because she know she should keep her temper not to hurt her subordinate (see how you can combine "not perfect" with "trying to be" ?). If this happens too often, she dismiss the PCs to protect them (and she don't hand out them some random gift she intended to offer: the encounter is a failure). I'm sure there are a lot of other ways to an OK encounter.
Or,
the encounter could have been a cool encounter with no stake and no danger, designed to enlarge the penis of the players (a goddess invites them just because she want to spend a few time with them ! And she speaks with a lot of respect, she admit she need them and they're doing something she can't do, she even tolerate some of their fancy behaviors !) instead of the penis of the MC. The two pages of the encounter could have been spent into fellatio advice to give the most possible pleasure to the players, and into explaining how to handle disruptive PCs without the use of violence, instead of a nonsensical life-or-death lolrandom quizz. (The very first step to handle disruptive PCs is to give them the choice - to invite them instead of abduct them. They may decide not to come, but if they answer the invitation, they know it's their decision and they should do some efforts). The main problem of the encounter is its mere philosophy, the general Paizo philosophy : use any occasion to remind the player about how small they are in their pants.
Now, if someone is good at subverting images, he can create a "respect my authority"-iomedae and create a fake poster or cover for the AP. It would be useless, but funny.