>>It seems that the solutions to the problem might look brutally ugly
Really?

Yet another voice here joining the advice "fix it" instead of throwing it away or cheating.
First try to fair the stern section as much as practical to make it symmetrical. If that does not do the trick, as other said, add a small fixed skeg.
For the idea what that skeg should look like go to
http://www.marinerkayaks.com/
Then choose MARINER XL from the blue bar on the left. Take a look at the picture in the middle of the Mariner XL page.
Skeg like that should do wonders for tracking.
Keep in mind that even a small amount of skeg mounted a the very end of the boat has huge effect on tracking, so your skeg won't have to be huge.

As far as looks...
perhaps this fix won't look too bad after all. It will certainly add a character to the boat.
Still, if you don't like it, paint it. Paint just the hull. The deck is the most visible part of the boat, so no need to cover it.
Hull painted, say, bright white + beautiful wooden deck looks stunning IMHO, much better than all-wooden look.