Since this is a new GOSM, are you using the new smoke box, cast iron thing with the removable lid? You might think about switching to a cast iron skillet. Most of us with the GOSM have. Seem to get better results. 2 hours seems about right. It depends on what type of wood you're smoking, as in sawdust, chips, chunks or bigger pieces of wood. I personally use a mixture of chips and chunks to get the smoke started, then the chunks take over and if I've got bigger chunks they seem to be last. And to further confuse you, I toss in pellets once in a while for added flavor. (There are several types of woods I can't get in chips/chunks, so I use Traeger pellets to fill in the gaps).
Your dampers sound about right. Remember, you want a thin smoke, not the heavy rolling smoke.
Refilling the wood? Well, after about 2-3 hours, I quit applying smoke. Time for heat and other magical steps to take over and finish off that fine piece of meat.
If you have other questions, please ask. These guys here are just brimming with knowledge to share.