Just found this thread and I have the same background from a WSM and am having the same experience with my Primo (oval not kamado).
While I know it’s sacrilege, I started a cook this morning and when I see the smoke die down a bit, I’m using a poker to sneak under the grate and deflector plates to disturb the coals and wood chunks. I know this is going to burn the coals faster and I’m having to cook and control a higher heat (260-270 range) but it is helping to relight the wood for a fuller smoke. I don’t want billowing yellow smoke at all, but do want more than the thin blue. My WSM did produce a stronger smoke flavor (which I like) and the ~10 or so cooks on my Primo have been more mild with thinner smoke rings.
I’m going to research the smoke pot, but wanted to add my experience here as well.