Learn English – Why is “biblical” the only proper adjective to not use upper case

Perfectly good would be different than saying completely good in most contexts: perfectly good tends to be used in a hyperbolic sense, meant to signify something that's "good enough". For example, that apple is perfectly good to eat is not the same as saying that apple is completely good to eat: the apple might have some flaws, but none that would prevent it from being eaten.

Which leads to the point that you'd only want to say something is completely good when there is no chance for it to be bad. Completely good is not a good substitute for very good or really good, which merely mean that something is notably good, not entirely or absolutely good. But, the Christian God or a saint would be characterized as being completely good because they aren't even remotely evil by definition.

Finally, if you wanted to say something was good in the superlative sense, completely good would be wrong. The correct word would be best, as in that course of action is best not that course of action is completely good.

In short, your only option seems to be exegese (or possibly exegeze, but probably not), if you must have a verb that would be acceptable to the OED.

But it should be noted that, for what is probably the majority of words on -sis, no verb is ever used; perhaps recasting your sentence would be a better idea, e.g. she interpreted the passage. Using the Greek infinitive exegeisthai is a bad idea that will send classicists off screaming.

The only traditional way of forming a verb based on a Greek word on -sis that I am aware of is -se:

Parenthesis => parenthese

Diagnosis => diagnose

Paralysis => paralyse

Basis/-se => base

Metamorphosis => metamorphose

Occasionally, modern forms on -sise are created, as in those based on -thesis (hypothesise, synthesise); I can't think of any other example. Those few Greek words on -sis whose noun-equivalents already end on -se in English also use -se for the verb, as in phrase and base.

For forms on -ise and -yse, you may encounter -ize and -yze in America, respectively, and possibly sometimes elsewhere too, so exegeze may be considered a valid alternative depending on your local tradition. However, this strictly has nothing to do with the formation of an English word based on Greek, but rather on regional variations within English. Lastly, I do not believe Americans normally do this with words on -ese/-eze (they stick with -ese: only after -i- and -y- is this z commonly used), but that's your call.

Your examples ostracize and baptize are different, because they have somehow retained or regained the z that was originally there in Greek (ostrakizein, baptizein), as opposed to in exegeisthai and most other verbs. The same applies to apologize/apologizein. This confusion is the reason (most?) British publishers and style books use -ise/-yse for verbs based on Greek nouns on -sis (Oxford and Cambridge alike, I think), like analyse; but they do often do use -ize for other Greek verbs, like baptize, and for words taken from non-Greek stems, like immunize, realize, colonize (either Oxford or Cambridge—I forgot). They usually do not, however, use -yze where Greek had no -uzein (so practically never). I know, it is a bit tiresome having to remember the exact origin of such words—I am usually too lazy to do so, I must confess.

The -i- in *exegise/exegize is not really defensible, because that is normally not done with words derived from -esis, but only with those derived from -isis. The -ize in energize comes from Greek -(e)izein, as energy comes from energ(e)ia; the -i- in apologize from Greek -izein as in apology, from apologia. The -y in English represents -(e)ia in most Greek (and Latin) words, and hence nouns on -y in English have verbs on -ise/ize.