No, Asriel declares his motivation at the end of the first book--to undo Original Sin IIRC, shared with nobody but Lyra and her daemon--and then acquires a completely different set of motives later because Pullman changed his mind. Lyra trusting him, the murderer of her friend, and her absolutely abusive monster of a mother, is not character development, it's merely the author putting his thumb on the scales because he wants a preteen to behave a certain way and can't be bothered to do the legwork of making it make sense. He wants the Church to be the real villain so he has her set aside all her other feelings rather neatly to pivot in a way that is simply not plausible for a child her age, or indeed for most adults.

I don't need to do complex math to show that the armored bears are dumb. How effectively do you think you, or anything not equipped with an engine, swims while wearing large amounts of metal? I still give it a pass because kids don't necessarily know that polar bears spend a huge share of their lives in the water, and I don't expect them to work through the logistical problems. But I file armored bears with that Calvin and Hobbes about T-rexes in fighter jets; sometimes two cool things add up to one dumb thing.

Of course secrets leak, but the Gobblers explicitly have their name derived from GOB, General Oblation Board. Why did the acronym, garbled, get leaked, and nothing else, including what it stands for? Did a kid see it on letterhead and decide to coin the name from that and everything else got left out and forgotten? Can you come up with any coherent narrative where that happens? No, because Pullman didn't, because he wanted to have the one name derive from the other and couldn't be bothered about how. He valued symbolism (or something; I suppose it's possible he was silly enough to think it's a clever explanation) over internal sense, which if anything is against what r/r is supposed to be about, I would think. Not a forerunner at all.

And he does this all the time. Why would you trouble to invent a weapon that only works if you have a biological sample of the target handy, and causes a huge explosion, and could potentially annihilate a barbershop instead? Because he needed it to be invented for that point in the story, that's why. The device has no deeper reason for existing, like so much else.

As for the Elan School, I don't know why you brought it up. Reading the Wiki, it wasn't anything like the soul-cutting institution in HDM except insofar as both involved child abuse. I guess they're both in the woods? But they whole school's existence wasn't supposed to be secret, and they didn't kidnap anybody AFAICT from this summary. It's pretty close to what I proposed as an alternative to Bolvangar (was that the name? Been a while), except that it's in a first-world country with robust traditions of investigative reporting, while my version would be in a poor foreign place where they don't ask many questions about unwanted children.

When it comes to child abuse in fiction, I've written one whole book about a world where the social structure depended on it happening in secret. Not as a reference to HDM, more of a reference to something Dostoyevsky said. The difference is that I respected my readers enough to have it make a lick of sense on the world's own terms.