Do you think an air filled barrel acts like a diver who is positive on the surface yet sinks past a certain depth?
I don't think so. The only way that the buoyancy of an object changes if if the volume of that object changes.
A diver's air filled lungs compress as he descends, occupying less volume, and providing less buoyancy.
An air filled speargun is a rigid structure by comparison. If the barrel is 1.000" in diameter at the surface, then it should be 1.000" in diameter at normal diving depths. If the weight does not change, and the dimensions of the gun (volume) don't change, then the buoyancy of the gun should not change.