Mind you, as you look through Garner, Fowler, MWDEU, and language authorities whom you reckon by the dozens on the subject of the split infinitive, you will not find them treating what the AP Stylebook imagines is a problem with splitting a compound verb. That is because placing an adverb between the auxiliary verb and main verb is perfectly idiomatic English, and has been so for half a dozen centuries and more. The authorities do not identify a problem there. If the split infinitive bugaboo is nonsense, then the split compound bugaboo is a fortiori nonsense. John Bremner dismisses it in Words on Words: "Those who would ban splitting a compound verb are even more antediluvian than antisplitinfinitive troglodytes."