Before you do anything drastic, I agree with Tom, it sounds as if the thread is stripped. For some reason, most likely cost, Fender have in some of their instruments over the years had some crappy truss rods, I have replaced the nut on one with a cap screw that I silver soldered in as the original was useless. Get the rod checked out, if yo can remove the nut yourself have a look and you should be able to see if the thread is stuffed. On some you will have to drill out the dark wooden plug as it covers the hole with only enough room for the allen wrench. Do this carefully, what I do is use a small bit of stainless tube as a guide, I use 1/2 inch and a drill that is a fairly good fit inside, 7/16 from memory without going out to the shed to check. Use a long series drill and do it by hand, go slowly and you will be surprised how easily it removes the wood.
Be bloody careful too, if you bust it, the wood won't grow back.
Your best bet is still a reputable tech, as far as heating a neck goes, I have done solid maple ones by steaming but would not be keen on doing the same to a rosewood fretboard as it is glued on and the heat will melt the glue. Unless you know what you are doing use a tech, and one more thing, just asking, are you sure you tightened the truss rod the right way, it has happened before.
Good luck
Clive