I gotta admit, I chuckled a little at the solar distillation idea. It would totally work, but man, now we're talking some sort of super survival or living off the grid thing, not hiking and backpacking! That would be a heck of a good way to do it though. I had this picture in my mind of the guy from Life of Pi floating around with his little desalinization floaty.
I know I already said it, but just to further qualify the statement, I've tried pretty much every type of reasonable backpacking-style purification methods there are and the only one that truly knocks out bad flavors is charcoal like that found in a First Needs XLE. Many times I've had the luxury of having two filters in the group so we got to compare immediately the funky flavor from a typical ceramic filter to the charcoal. I haven't done a side by side on the newer hollowfil glass fiber filters like you find in the sawyer and most gravity filters, but I can still taste flavors in water from them so I'm sure it doesn't knock it out like the charcoal ones do. I don't take it with me on all of my trips, but if water has potential to taste like ass, it's the hands down winner.