wished God wasn't such a dick (second order).

This is not second order. It's just D(God approved of homosexuality). If he himself were God, then it would probably be second order, but just wanting the rules to be different is first-order. Similarly,

Larry was brought up to be a good Christian, and desperately wishes he didn't wish God was anything other than He is (third order).

is not third order. Third order gets weird. Third order would be that Mimi wants heroin, and in fact, wants to want heroin, (if you offered to magically make her not like heroin, she'd emphatically decline), but on top of that, she wants to want to not want to use heroin. Maybe she doesn't have a problem with it, but her friends do. Maybe she would be well served if she could express an honest desire to quit while not actually quitting. Third-order desires get pretty confusing, though I may have just explained this one poorly.

Furthermore

I imagine our desires are less like a logical hierarchy and more like a food chain. On any given day Larry's libido could be the biggest fish in the sea.

is not exactly in line with the post. I don't think there's any claim that these things are a logical hierarchy. One can have extremely weak first order desires and extremely strong second order desires, though the latter will tend to consolidate into changed first order desires if they are strong enough.

Second order desires do often stem from conflicting first order desires, but what determines the order is the object of desire (if it itself is about a desire, it's 2nd order, and so on), not its magnitude.