Alright boys... As promised, I fought the heater this weekend.
It was a long fight, going deep into the 15th round.. but...
I won.
It took a patient strategy. I started with trying the heating and cooling method, but could never get a good enough grip to do any real work. So, with a slight fear in my heart, I turned to the drill with left hand bits. I started small and made sure I had a good, straight center hole. I worked my way all the way up to 1/2". At that point I tried getting a 1/2" pipe extractor in there. I got torque, but it wasn't budging. I moved on up to 5/8" and still no luck. I tried chiseling at that point... no luck. So, I went for the Hail Mary pass. I put on the 3/4" bit and went to work. I was able to then work a 3/4" pipe extractor in. It made a very solid bite. I got my breaker bar and hung my 230lb self on the end of it. Like a gift from the heavens, it broke free.
I still don't know why it was stuck. It was not cross threaded and I did not damage the threads with the drill. A new anode rod went right in without issue. The old anode rod was about gone and did break off in the process, but it shouldn't be an issue.
So, lessons learned:
1. You don't have to torque an anode rod in like you are a gorilla.
2. Patience and power tools are your friends.
3. Buy really good drill bits. I bought cheap ones at first because I didn't have a left hand set. I ended up breaking down and buying some good titanium coated ones to finish the job.
I appreciate all of the help and advice. Seriously. Thank you. Really glad I'm not putting a new heater in this weekend. I think I'll go camping instead. :B
Here's a link to the removed rod, just for fun:
https://postimg.org/image/s4lix6l69/