Suppose I have this intentionally strange-sounding (and perhaps ungrammatical) sentence.
Finante faru ĝin!
Maybe even this one.
Faru ĝin! Sed finante!
That is to say, "Do it, but finishingly so!" or "Do it, and finish the task!". Beware that this is only a question about grammatical correctness and not about good practice. If I were to actually communicate the idea, I would not say it like that.
That aside, in my question, the adverb here does not necessarily need to pertain to "fini", but any transitive verb. Why transitive? Because I feel like the "finante" in the two sentences are missing an object, unless it shares it with the "faru", and I am curious about what the rule here is, when the adverbized verb is transitive.
Unrelated to transitivity, the "-ant" in the "finante" implies the present tense, when I am using the volitive mood. Dunno what to do about that one without using a neologism.
Speaking of which, if I really had to come up with something, here's something wild, even stranger-sounding, and probably should not be used in actual conversation.
Finentece faru ĝin.
With a "-entece" ending analogous to "-antece" and "-ontece", as in words like "estontece". This way, it would no longer seem to require an object (or subject complement in the case of "estontece"), and would no longer imply the present. But, again, I know this is probably kind of abusive of the language, but hey, it's fun!
finante
meanswhile finishing
(what?). There is way to say what you want to say, and we can help you find it but first we have to know what it is you want to say. It seems you found a structure, built a sentence and tried to assign meaning to it ...