I cannot find the whale (more specifically, the whale cannot seem to find me). I've criss-crossed probably 50 times or more, but only gotten tired and drowned, arrived at the island or back on shore or got eaten by the shark. All walkthroughs I've found seem to assume the whale will come after just a few crossings.
Any help appreciated.

I think you must just be really unlucky. I am waiting for a similar random event to happen in KQV and it is taking me forever. Having said that, I personally was lucky with the KQ IVwhale and never got eaten by the shark - it appeared for me in a few crossings.
Good luck!

There are certain things you need to do and items you need to have before the whale will appear.
This could be your problem.
I'm not entirely sure what those items/things are (it's been a while), but I think you need to be trying to get the unicorn and have the feather. You may also need to do other things though.
[edit] I also seem to recall swimming west from the pier being a good way to go... but again, not entirely sure.

I found it on my first try with these parameters, although I'd suspect having the feather alone would be enough to trigger it. But considering this thread is from 5 months ago, I'd expect he found the whale by now.

The whale won't appear until you've visited Lolotte for the first time, I believe.

And just in case, you should probably get the peacock feather before then...

I know this is old, but THANK YOU. I had been avoiding her place assuming something bad would happen -- but right after I did this, the whale finally showed up for the first time after two swims.