what color is the smoke you are getting? if it is white I'd guess that is where your bitterness is coming from. Also is your wood stripped of bark?
I would suggest smaller wood or chips and add them before you put in the meat. Let the heavy smoke "burn off" and add your meat when your getting just the smallest amount of visible smoke.
I am guilty of using too much wood and or being impatient. And it does make for a bitter taste.
Your looking for a thin bluish smoke, you don't need much. As long as you can smell it you will taste it.
Not sure how this would work out but you could buy a $6 bag of lump charcoal and light one of the bigger chunks, just on the end, and add that to your cast iron skillet. My thought is one lump won't cause you any temp problems, it is real hardwood so you should get some smokeyness from it as well. You might get more smoke time from this than you do from your chunks ( perhaps your chunks only smoke while the burner is running full bore trying to get the smoker up to temp, then the burner may not run hot enuff to burn your wood while it only has to maintain a cooking temp ).
hope you followed my train, it can be hard to do!