Correct me if you think I am wrong, but...
Classically, a trained swordsman would beat an untrained peasant holding a sword 99 times out of 100. A trained archer is going to make a better shot than someone with no experience shooting a bow. This all changed with the introduction of guns. You can train and get better with guns, but for the most part, it's point and shoot. Guns offered a much greater equalizer between forces.
Let's take a look at our classes. Each class can take 1 tool from the others, and 3 of their own. This gives 2 possibilities:
1. There is only room on the ship for each person to take a total of 5 tools. This seems unlikely. Given the infinite ammo we have, along with how useful certain things would be to have realistically, captains would make room for a few extra tools and ammo types.
2. Each person is only trained in how to use 5 tools.
Here is why I like option 2.
Trained pilots know how to use 3 different piloting tools. They can shoot a gun, and repair things in a pinch, but what they know how to do best is pilot.
Trained engineers can use 3 engineering tools. They also know how to use a specific type of ammo. They can take the wheel and lumber around because they have no training, and they can take a gun and shoot it pretty effectively, but what they know how to do best is repair.
Trained gunners know how to use 3 types of ammo. They can take the wheel and steer around, and they can repair something in a pinch, but what they know how to do best is use a variety of ammo.
Piloting a ship takes skill. Truly piloting requires the deft use of tools and requires a pilot. Flying a weapons platform can allow you to take a different class, but in that case you are a stationary weapons platform, not a mobile craft. Piloting practically requires a pilot.
Repairing a ship takes knowledge. Repairing something complex requires knowledge of how it works and goes together. Someone without that training is almost as likely to damage it as they are to fix it. Repairing practically requires an engineer.
Shooting a gun takes... a trigger. There is a level of skill involved, but my premise is that guns are an equalizer. A gunner is more versatile because he can use more ammo types, but an engineer can shoot just about as well and can also repair.
Just going by in universe logic, I would argue that gunners should be the least used class. It is an opportunity position to add versatility to your guns with the large tradeoff of being nearly useless everywhere else.
In keeping with this idea, I would argue that gunners should get a slight boost to accuracy somehow. Whether that is through the rangefinder, a lessening in recoil, or a lessening in spread. But realistically, you would not leave port with more dedicated gunners than engineers who are willing (and happy) to take a gun.
TLDR: Pilots need training, engineers need schooling, and guns are easy to shoot. Multiple gunners should never be worth more than multiple engineers.