There is not much you can do here IMO, folding seems out of the question as played.
The only suggestion I would make however is to go way larger on the river. If we are ever beat here then we are going broke, however if we are getting paid here villain will almost always be showing down Kx and people hate folding trips. In this pot we should be going pot at the absolute minimum, and I would be opting for an overbet here almost always as villains lone Kx hands will have a very hard time finding a fold. And as pointed out, if we are beat it does not really make any difference as we are usually going broke anyway.