Sci Fi, MG, Ambassador Son, Alien Planet, Swept into Prophecy/12 Tasks ("William Tell",etc)

[Dave Lindquist]

I'm trying to remember a science fiction book ('MG', I guess? Just under young adult, but after the true children's books) involving a kid (son of an ambassador) on another planet. This one is a '12 tasks of hercules' type of plot, but with a teenage kid as the protagonist.

Basically, the plot is:

• The kid is the son of the ambassador to this planet.
• He is somehow separated from his dad (the ambassador) and ends up in the hands of the aliens.
• The aliens are somehow in the grip of a government that is not exactly the most benificent, and have a myth (prophecy?) about someone who will come to "save" them, and the 'tasks' they'll accomplish that will prove that they are the one.
• The boy somehow ends up in the position of doing the first task, which is a 'William Tell shoot the apple off of someones head' trick. Since he knows he is not that good a shot with a bow, he waits until fog rolls in (convenient timing) and shoots the arrow out to sea -- he's going to claim that he just missed, and they won't be able to find the arrow.
• However, the antagonist has anticipated this, and does a sleight-of-hand swap with a split apple and arrow, so the kid ends up succeeding on the first task.
• After this, he is kind of swept up in the events. The antagonist is using him for his own ends (can't exactly remember what those are), and has plans for him to succeed almost all the way, then die in the last task.
• The last task (if I remember correctly) is surviving in some caves through high tide (they are completely submerged at high tide). By this time, the boy is planning out his tasks, and has figured out that in one cave there will be a compressed air pocket that he can survive in (he carries in an inflatable bladder to help him float).
• The bad guy somehow arranges to try to kill in him the cave (can't remember how), but he manages to escape.
• I don't remember much of what happens after this, but the general plot is one of someone being swept into a prophecy by faked successes, and finding out that the prophecy has a mind of it's own and doesn't care about the fact that it was faked.

Other points:

• This would probably have been in the mid-80s
• There was a 'purple' theme -- the book cover was I think very purple (hard-cover with library glossy plastic add-on cover). I believe that it had ocean and dark clouds on it.
• I remember this being in the library stacks not too far off from Andre Norton. I think maybe 'before'? It was definitely in the "kids books" section (think Hardy Boys, Andre Norton, Enid Blyton, etc), in the science fiction grouping, where Andre Norton's "Defiant Agents" was.

Any hints or ideas? (Thanks!)