Whale sharks don’t do stationary target feedings they do moving filter feeds similar to what basking sharks would need:
The suction feeding capability of Whale Sharks allows them far better intake of food than how the same method would work for a Basking though.
Leatherback Sea Turtles are impossible to keep,
There has been quite a bit of success in research facilities by using harnesses attached to an overhead rig; however it doesn't exactly make a great exhibit.