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I would be tempted to add a couple of strips of wood, one either side & then add some taper from front to back, by the time you round the corners & fix all you metal & spear, the gun will sink!
We are talking about balancing the gun to hover in the water, not float with the spear in place but just remain static at say 5 mt depth! The gun should pop to the surface without the spear & be neutral in the water with the spear in place.
Not many commercial round barrel guns have this asset but most wooden guns can be set up to balance just how you want.
You may prefer a slightly muzzle heavy gun but you don't want a heavy muzzle that pulls the gun down.
I guess you could still say a balanced gun will sink but it will only just about sink! The one in my picture above slowly turns over in the water if you let it go & then begins to slowly sink or move away in the tide.