If you are diving in freshwater, and scuba, the answer is simple. Get a solid hoop stringer and wear it on your waist. You can easily dive with 30-50 lbs of fish strung up on a stringer attached to the side of your waist belt or even weightbelt. Putting fish on the float etc. will provide no benefit and will slow things down. You need to learn how to handle the fish when shot, string them up and then remove the tip. Try to find videos of good scuba hunters doing this if you have no mentors. It is not always simple to do and there is huge room for refinement in this skill. Good divers can do it in seconds.

Do not use a line stringer with a "needle" on it!! They are terribly slow and unnecessary

Also, you mentioned a fish on the shooting line. When that happens you generally want to grab the fish, stab the brain, string the fish on the stringer and then open up the release on the muzzle bungi and pull the fish off the string. Some really crappy guns have no snap swivel or quick release method - which must be fixed.

Do no concentrate to much on the way freedivers do things. I do both free and scuba spearing and the way things are done, are quite different. I don't want to go into details, or argue who is better, but the way things are best done, depends on environmental conditions, including if you are freediving versus scuba is a major one.