I too have a Chargriller set up like yours I bought over a decade ago and still use (last night to grill steaks as a matter of fact) to grill and I have a rotisserie set up I use as well. I've since moved on to a uds but what I did to get a fire and good constant temp (I showed this to my brother in law and he does this with great temps and results) was to place a full chimney of hot charcoal brickettes on the fire grate of the side firebox and place large split wood on top. It worked for me to fill the side firebox with three or four large split pieces of hickory. My brother in law fills it as full as he can. Try experimenting with a method such as this and see how it works for you.
Smoker Joe, UDS, Weber Silver 22.5 kettle, MB Gas Smoker, CG Smokin Pro w/sfb, pitmaster IQ110