Theres a few threads on here on how to make the clear pvc float line using the line and a mono through it, crimped and sealed at the ends. Looks to work quite well and also the line itself floats wich is a bonus.
I use 5m of bungee as a floatline when hunting in the kelp or in shallows with rough waters, you can easily dive to about 8m without to much strain from the bungee and if you hit a big one the bungee playes well. Also its pretty rigid and doesnt tangle easily. When we dive off a boat I have a line winder with 15m of rope line to the float and the 5m bungee going to the gun. If its not too kelpy it works a charm as you can roll off as much line as you like.
Back to the stringers, I either string to my float like Covert or I just made a bodyboard float with a stringer and net bag on top, fish gets strung and goes into the meh bag effectively keeping them from being eaten by gulls as well as keeping them out of the water

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Dive safe and shoot straight
- Hénré -
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"Thinking is the hardest work there is, which is probably why so few engage in it"
- Henry Ford -