Great questions!
Without seeing your exact set up, it's hard to pin point exactly what could help.
The basics of temperature management of any BBQ is basically air flow Vs amount of fuel.
Your doing the right thing with trying to control the temp with the dampers, but if the BBQ isn't very air tight, it may be difficult to keep it down.
One of the best methods I found was using The snake method, this works well as it limits the amount of fuel that can set light, so even in leaky bbq's it should help keep the temperature down.
If you get spikes in temps, you can try to add a bowl of cold water, as that will absorb a lot of heat. I wouldn't personally try adding wet wood as it can smoulder and create an acrid taste.
The best thing is to try changing one variable each time and see what works for your grill.