You did it just right. And you were still smoking the meat even though you didn't see smoke.
After the wood has burned down to a coal stage, it continues to burn and put off smoke, but it's a light smoke, in some ways a pure smoke. When the wood starts to smolder/burn, the first things to go are the volatiles, things that tend to make the smoke smell most like the type of wood it is. This smoke is darker, denser. And it usually contains some creosote.
Consider a pine log. When it first catches, it crackles and pops and puts out thick smoke. But as the log burns down some, it calms down and cleans up the smoke a bit. Same for charcoal briquets. When they first light up, it's smoky as all get out. Then it calms down and it's ready to cook on.
As the fire progresses, the smoke dissipates as the fire consumes the lignin and main contents of the wood. As long as there's not just ash, you will continue to produce flavorful smoke, but all you may see is just wisps. And that's the perfect level of smoke. Not too strong or too much, but just right.
A total smolder isn't really desirable either. This kind of fire produces the most creosote and that tastes awful.
Soaking is fine, it tends to make things last longer.
Not soaking is fine too.
You might try some of the chunk wood and see how that endures. A 1x2 piece should smoke for about 45-60 minutes if you can keep it out of the flame of the gas burner, but hot enough to light up and keep burning.