The problem I see here is that you want to encourage people to use weapons which are less popular. Well, they are less popular for a reason, may it be that they are weak, they work badly or they are having more enemies that have a resistance against them.
I for my part use Neutron gun, Plasma Rifle or Utensil Poker most of the time. They are the easiest to use and also have the most utility. Neutron gun is a straight-forward DD, while utensil poker is more used for spread out damage. Plasma rifle is a boss killer anyways.
Instead of trying to encourage people to use less popular weapons, encourage yourself to check every weapon’s functionality and review their power. I can tell you once thing, the DPS on some of them is rather underwhelming. Like, why is laser’s range capped? Doesn’t make sense. A laser goes on and on and on.
Or, in the worst case scenario, make weapon modifications possible. Give your ship an initial weapon slot you can put things into such as items that increase the projectile speed, or that give x2 projectiles for half damage per projectile. Stuff like this. Make weapons mod-able so people can find good combinations for weapons. Make weapons research-able to make them initially better for yourself.
We were talking about that on the discord and making weapons work like this is straight up useless.