I use the store bought chunks/chips myself...it's all I can get for now...let's take a closer look at what's happening in your smoker...
What do the chunks look like when the white smoke stops? Are they completely burned-up into grey ashes, or does it look like a chunk of lump charcoal?
If burned-up, you have to reduce the amount of air getting to the smoke wood to slow it down to a smolder.
If it's like a lump of charcoal, and you put higher heat to it, it should start smoking again...this is what I try to get, even if I use fine chips instead of chunks...blackened smoke wood, if you will.
If this is the case, try a cut-down metal can(short enough to fit between the smoke pan & water pan) to put the smoke wood into, and if you have the top of the can you could lay that in over the smoke wood as well. Be sure to burn-out the can really well and clean it up before putting it into the smoker with heat. Coffee can or large vegetable/beans can works. I've done that alot on my SNP sfb when I still had the propane gas burner in it...worked like majic.
Hope this gets you headed in the right direction...