If the unit has 2 burners, put the wood in an old pan on one side, with only that burner going, on low. You will slow cook then on the other side if you can keep the overall temp down to 300 or less.
Sure, use a box with holes to put the wood in. That keeps the crud out of the burner orifices. You can do that and put the box under the grate and free up more space for cooking.