I had a foster with this problem. She'd also fixate on lights, reflections, and floating dust specks in the sunlight.
Once she had difficult, engaging work on a regular basis, her compulsive behaviors decreased greatly. For her, that was sheep. For another dog, it might be scentwork or tracking or something else challenging.
When she was here, I interrupted her fixating behaviors by slamming doors, dropping a heavy book, that sort of thing. Redirecting is one approach, but if you're redirecting by giving the dog attention, it can become a reward, instead of simply an interruption in the pattern of bad habit.
There is a lot of research out there about how compulsive habits are formed, and much of it agrees that interrupting the cycle is key. Some describe it like the brain is stuck in a "loop of wrongness", and the longer it goes on the more difficult it is to change.
I would absolutely get her involved in training and difficult activities that really make her think, struggle, and learn. Basic pet obedience is a piece of cake for these guys, they're capable of learning much more complex things and using their brain every day.
It's one thing to snap at a fly here or there, but if this really is an obsessive behavior, it won't get better if it's allowed to keep going on. When it gets bad, it's difficult to live with.