You don't dictate against a moonballer,
you just try to stay in the point.
Trying to short hop / half volley a moonball on the baseline takes years of training
And the 1 in 10 you get over the net, he is waiting to volley it away, and you have almost zero control on this reply
It's a lethal strategy, and that is why he's undefeated.
by the description of the moonballers you are giving, it sounds a lot like Nadal in disguise.
Jokes aside.
It all depends on your skills and on your opponent.
1. assuming you face a real pusher, who never tries to hit winners and is afraid of the net:
if you lack the overhead, and don't want to practice it in real match, then against a true pusher you can play half-volley / hit on the rise.
you don't have to hit winners, just keep the ball in play.
your answers will be all over the place, which will mean that the pusher has to run a lot and work with "junk balls"
2. if you lack overhead, then against same true pusher you can hit the "drive-volley", which is almost identical to the forehand / backhand, but you don't wait for the bounce, you hit in the air
you'll probably end up as well hitting a lot of mixed bag balls, junk balls, ok balls, so your pusher will have to run a lot, but as the pusher by definition doesn't try to hit winners, it's ok
3. if you lack overhead, then against same true pusher you can hit the volley. Yeah, it's gonna be from somewhere close to the baseline, but that's ok
4. practice overhead, approach the service line, and hit overheads from there.
No need to crush winners.
You are essentially "stealing" time from the pusher, so while the moonballs / lobs will keep coming at you at slow pace and give you time to set-up the overhead, the opposite is quite different. The overhead smash will be coming back to the pusher much faster, simply because the ball will be travelling smaller distance
5. don't forget drop-shots, short balls, etc. As per your definition of pusher, all they can do is send deep moonballs from baseline.
Once they have to hit the ball at the net, they might simply lack the skills, so why to play their game?
6. If your pusher can hit the baseline (+/- a foot) 10 times every rally, and meet you with good passing shots when you simply approach the net, perhaps your opponent is not a pusher, perhaps it is a good player that identified your weakness and is simply using it