But... you guys are inventing the idea that you have to not interfere in order to stay hidden. I'm not trying to insult here - inventing is good. You just don't have to do it. You can invent other ideas instead.
Rules-wise, interfering with a ranged attack is a trivial thing. It takes no action. Hostility is not an action. It's a state of being. Rules-wise you do nothing but stand there with hostile intent, and BAM, she's got disadvantage on her shot. You do nothing that under the rules for hiding will reveal your position.
Obviously, to all of us, that isn't satisfying in itself. But that's okay! D&D has always planned for that! You make up stories. Sure, you can also ignore Rules, that's fine. You just don't have to. You're making up the story anyway, so all you have to do is make up one where it works.
It's a lot easier to do if you're not absolutist. Start from the idea that combat is chaos and no one is perfect or has a perfect plan. Both the shooter and the invisible guy are just doing the best they can, without any master plan. They're both not 100% perfect at what they are doing. (To me, this is important for realism - everything else is fantasy).
Shooter tries to shoot. Invisible guy tries to mess up the shot. Both have many, many, MANY ways they can go wrong or right. I could literally spend hours coming up with scenarios to describe it, but the only important one would be one that actually happens during play, and you NEED all the factors in play for it to really matter. Who's the attacker? Who's invisible? Who else is there? Where are they? What just happened last round? What led to this odd situation? What's the terrain like? The weather? Etc etc.
Then the big one: What does the shooter roll on the dice?
I will use ALL of that to justify what happens when shooter goes to shoot and the hostile guy (invisible or not) tries to mess up the shot. The roll of the dice is ultimately most important, because if the shooter HITS ANYWAY then it doesn't really matter what the invisible guy was trying to do. Whatever it was, it didn't work. (I'm not saying that I wouldn't imagine what the attempt was, I would, but it's not as important when it isn't effective).
Maybe invisible guy WAS going to do something that would give away his position, but missed (like try to hack the bow with his short sword, but was too late - shot passes over his shoulder, so he changes tack on the fly and remains hidden).
Do what you like, obviously, but I personally would rather keep the fiction open and wild and the rules tight (ish - I am far from a rules lawyer). It manages expectations better (IMO) to have the rules remain what the player has read in the book, unless the scenario is entirely unworkable (which I don't think I've seen in D&D - I have seen it in other games.) Or your group is one thar plays with a lot of house-rules.
My conclusion is that this rare scenario does not need rulings to make it work - it needs dynamic descriptions. YMMV.