Probably need more information. What kinda rig do you have? Is it a smoker or a gas grill? With most gas rigs, you should be able to make some kinda mod so that you can put a wood chip/chunk box of some kind between the flame and the food. A metal cake pan or a coffee can will keep the wood from flaring, but will provide plenty of smoke.
One problem is that gas grills are not designed to trap air or smoke like smokers do.
I'd look for ways to plug up the air-flow and trap the smoke produced long enough to flavor the meat.
Heavy duty foil might work for this.
I don't think you'll have any luck getting wood started then turning the gas off. You'll need to find a way to maintain a slow flame that is good enough to keep the wood smoking.
There are tons of smoker-boxes designed to be added to gas grills. I'd start with one of those. It will likely be more reliable and predictable than just wrapping your chips in foil.
In general, thinner walled boxes will give you more smoke with less flame.