I think you have to stick with goat. There are more of the examples in which it works, than of those where it's a stretch. So, maybe try to stretch? Even if "old goat" isn't quite as rude as jackass, you could still get the idea. An attempt:

Take the billy-goat. He's a symbol of everything stubborn, a symbol of everything lascivious, and even a symbol of Satan. He is a scapegoat. Of course, he has his positive interpretations, such as when his is the horn of plenty. Or the goat as a fertility symbol. Though there, too, you have an allusion to the goat's sexual energy, and hence to lust.

What I most dislike is curses like "Go to hell, you old goat."** or the expression "Love is blind: you may land an old goat," or when people say that all men are silly billy-goats. "Goat" can mean sexually obsessive. Formally speaking, this symbol applies quite nicely to all my admirers. In reality, that is absolutely not the case. Even if everything they do is motivated by a primitive sex drive, they don't have enough of a goat's stubbornness, to follow through. Right now, however, I'm not talking about them. I'm talking about the goat.

** Variants to make it cruder:
Go --- yourself, you old goat."
Go to hell, you --- old goat."

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Note added at 2 hrs (2011-02-01 23:15:03 GMT)
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Reply to Mark: Yes, certainly. Not just "goat" by itself, but "old goat." Mild version, "Silly old goat." Cruder version, "F---ing old goat." Those both come pretty close to jackass.

Try searching "you * old goat" - but, not on the whole Internet, use Google books to get published examples. There are a lot of cases where the missing word stresses the sexual side: randy / horny / filthy / lecherous. But there are others, where it's more like jackass: stubborn / silly / crazy, etc. Not exactly the same, but it's a lot less of a stretch than trying to make this entire passage be about some creature other than a billy-goat.