Smokin Okie - thank you for the tip on being more aggressive with pushing around the coal/ash pile. I smoked a brisket for 12-hours day before yesterday and realized the problem I was having was not the coal bed growing too large, it was how is was arranging the coals. I was raking the coals into more of a pile thinking it was somehow the best practice. However, I believed it caused the coals to not burn well and the temperature to drop. As a result, I would add more wood and more wood created a larger pile of inefficiently burning coals. This time, I kept the coal bed spread out more along the bottom of the firebox and didn't get to crazy with moving it other and to stir it around once in a while. That allowed the coals to burn well and reduce to ash without piling up as much.
Since the wood I buy is cut anywhere from 12" - 16" inches long, it spans the width of the firebox and usually starts burning with plenty of space for air to feed underneath it and above the coals. And to answer the above question, I tried to use the grate that came with the smoker once... What I did not like about it was it did not seem to make things any easier. It actually made things more difficult for me. I had to lean over to see what was going on with the fire and not as much ash made it to the bottom of the chamber as I thought. So, I haven't used it since.