It's long past time to have a look at that verbs entry in the AP Stylebook, because, and I say this out of a spirit of concern and disinterested helpfulness, it can't stand up to examination.
The crucial part is this: "In general, avoid awkward constructions that split infinitive forms of a verb (to leave, to help, etc) or compound forms (had left, are found out, etc.)"*
Now you have every reason to know that that is fudge. You must know that, because the split infinitive is a superstition of usage. Bryan Garner labeled it that; it wasn't my doing. The Stroppy Editor recently conducted a thorough demolition. And Merriam-Webster's Dictionary of English Usage exposes the hollowness of the stricture:
"Critical opinion expressed in usage books appears to have settled on a wary compromise. The commentators recognize that there is nothing grammatically wrong with the split infinitive, but they are loath to abandon a subject that is so dear to the public at large. Therefore, they tell us to avoid split infinitives except when splitting one improves clarity. Since improved clarity is very often the purpose and result of using a split infinitive, the advice does not amount to much."
But wait, there's more: that vexatious split compound verb.
Here, I think, as with over/more than, we have a bogus rule invented by newspapers. I suspect that people unsteady on their pins with usage and syntax must have thought that if you shouldn't split and infinitive, then a fortiori,** it must be impermissible to split a compound verb. Thus generations of journalists have been schooled to think that "we always have done it that way" is correct and "we have always done it that way" is an error. Lift your heads out of the newspaper and look at how native speakers and writers have inserted adverbs between the auxiliary verb and main verb since Chaucer was in grammar school.
In Words on Words, the late John Bremner, after lacing into adherents of the split-infinitive hogwash, goes after the split-compound charlatanry: "Splitting an infinitive should not be confused with splitting the parts of a compound verb, as in "I have often walked down this street before."*** Those who would ban splitting a compound verb are even more antediluvian than the antisplitinfinitive troglodytes."
The sentence you adduce to support this utterly unjustifiable rule, "There stood the wagon that we had early last autumn left by the barn," is so ungainly that it is hard to imagine that even a journalist wrote it. The advice it ought to inspire, rather than to avoid splitting verb compounds, would be to avoid constructions that sound like literal translations from Central European languages.
A revised entry might run along these lines: verbs Split infinitives are unobjectionable and are often preferable to strained constructions that attempt to avoid them. Split verb compounds, with an adverb between the auxiliary and main verb, are idiomatic in English.
Pick your own examples; I don't want to appear to be dictating to you.
Now, if you should make such a sensible decision, you can expect that people will react, as they did to the over/more than post, that it "just doesn't sound right." Of course it doesn't, to them, after years of corrupting their ear for the language by reading and writing for newspapers. (That's also why using opt and tap instead of choose sounds natural to them.) Think of the children.
*Um, there really ought to be a period right there after the parenthesis to close the sentence, but I don't have the time to fix everything.
**Latin for "making a bad decision worse."