Interesting points and they make sense. I've been looking at caudal fins since I reacquired an Aqueon. Wondering if a thinner foil section might perform for faster, easier oscillations with lower air consumption. Say something like a tuna fin or maybe that of some marine creature with a fin beat rate that might be comfortably approximated by a human.
The current foils are fairly thick and shove a fair amount of added mass as you point out. There is the tradeoff between lift, drag and added mass vs. energy input and air consumption. I have no doubt Cal did a lot of development in these areas years back. Still, the candidate design was to have wooden foils which have to have a minimum sectional area to be strong enough to perform. Wonder what would be experienced with thinner, lighter foils of varying aspect ratios.
The spring supposedly aids performance until sufficient speed is achieved, I suspect until the vortical streets shed by the foils promote oscillation. I am not totally convinced though and wonder if some benefit is provided even at higher speeds. I was thinking of some form of spring tensioning, better still a spring replacement, that could be tensioned on the fly.
You are right, going full out in apnea is a hazardous activity. A minder closely paralleling your movement is a reasonable precaution.

A photo of the Aqueon on the Wreck of the Sapona off Bimini in the Bahamas. Shot a fair amount of still and video of the Aqueon within and around the Sapona. Hope to get things processed and uploaded soon.