Chemist doesn't even have to shoot real healing bullet. You can make them shot charged aetherial energy via bazooka or something.

Anyway, my idea of chemist is that it use special "gun" that have chambers filled different potion liquid. You can rotate those chambers if you want to change which potion you use. The chemist would need to use their aether to charge the gun, which will cause -insert whatever aether terminology here- and the gun will shoot condensed aetherial energy with the same properties as the potion, or combination of them. That way we can have battle medic who use potion, but still considered as magic user.

This may sounds complicated, but they can translate it into chemist gameplay as "chemist stand still to charge(cast) their gun and shoot their teammates with healing spell(aether energy witg healing properties, like gnb aurora)". Done.

I know their excuse is that they can't find suitable weapon for it, but somehow I have suspicion that it's more about balancing the healers issue.