Here's the modification I made. It's not really a charcoal basket, just a bent piece of $12 metal. But it lifts the charcoal off the charcoal pan that ships with the grill, allows better airflow, and makes it easier for the ash to fall away.
I did it as a test to see if it worked and it worked so well that I don't have any plans to modify it any further. I can attain much higher temperatures and sustain them for hours.
You can see in the picture that the grate that ships with the grill only has holes spaced about an inch or so apart. It may be that by tediously placing each piece of charcoal between the holes you can get a better burn, but you are still left with the ash.
Click on the image to see a bigger version.