Hi Chris, if your barrels aren't quite heavy enough, one of your pics gave me a thought... Have you tried a bit of elastic tied between your barrel pivots going under the back of the barrel in the turret? Maybe a bit of haberdashery elastic or a small rubber band looks like it might give enough bias back to down position (not knowing how stiff your pivot is but it looks worth a try!)? If you just use something like fishing line /thread to pull them up also -the band will pull them back down?
Rich