I'm not a Tinitarian and not even terribly religious. I'm just a person who thinks the Bible is a really cool book. (Who happens to be married to a JW) It's not a question of what I want to believe. I'm stuck with what the original text actually says just like everybody else is.
I don't know if this will help or just confuse things, but look at 2 Peter 2:16. It expresses an idea almost identical to what you're thinking:
"....A voiceless beast of burden, making utterance with the voice of a man, hindered the prophet’s mad course."
The reference here is to Balaam's donkey. "With" in this instance indicates possession. The donkey's mouth opened and the voice of a man came out.
The difference is that the phrase εν ανθρωπου φωνη (In the voice of a man) is modifying a verb of speech -φθεγγομαι (phtheggomai -- to give out a sound, noise or cry. In this sentence, "Making utterance")
At 1 Thessalonians 4:16, the phrase εν φωνη αρχαγγελου (In the voice of an archangel) is modifying a verb of motion - καταβαινω (katabaino - descend)
The voice of an archangel is not a method of locomotion (At least I don't think it is...) and the phrase therefore can't function like the similar phrase does above at 2 Peter 2:16. Try to focus on the fact that "In the voice of an archangel" is telling us something about the Lord's descent. The main verb determines how the subordinate phrases are understood.
Here's a way to look at it in English. If I were to say:
"MadJW descended the mountain with rope"
--We would automatically understand that you were the one in possession of and using the rope. "With" would indicate agency or possession.
But things get weird when the phrase has nothing to do with descending a mountain:
"MadJW descended the mountain with the sound of a 72 piece brass band"
The sound of a brass band doesn't move you from point A to point B. "With" in this instance would indicate accompaniment -- something that happened while you were descending the mountain
I've noticed that when it comes to the trumpet, JW literature has absolutely no problem with the rules of Greek grammar:
"Another thing that accompanies Christ's descent from heaven is the sound of "God's trumpet." (1 Thess 4:16) The trumpet in this case is not a war signal for assembling troops that they might fight and put the enemy to death. Rather, the blast of "God's trumpet" is a peaceful one for assembling Jehovah's people...." (The Watchtower 6/15/1979 p.25)
I'm not trying to be a jerk here and I'm not trying to drive you crazy by harping on grammar. We can't just clean out the library and throw the textbooks away when they all disagree with a particular interpretation.