Thanks for the replies...
I had another go-around with Klipsch customer service and cannot believe that they either: don't fix headphones in-house or, at the very least, wouldn't recommend a source that could. My headphones are certainly functional but the cracking around the headphones and the exposed wire wrapped in electrical tape is ugly.
I'll try the strain relief ideas and heat shrink the wire but this interaction has left me with a bad feeling about Klipsch. I mean, how hard is it to say: "while we don't do in house repairs, I recommend...". Instead the guy wrote "there is no way to repair the headphones without destroying them". Cop-out!