Yep, that's all the smoke ring I can get too. And if there's not a piece of that ring in the pulled mix, there's zero smoke taste.
We all have different tastes I guess, I get plenty of smoked flavor in my pulled pork, did even when I was using a Cook Shack electric smoker even though I didn't get as much of a ring.
And you might be surprised that:
"Although it adds no flavor, the pink band does look cool"
(quoted from a noted BBQ site, can be found on many of them...)
The smoke ring is actually a chemical reaction, you can use a variety of things to produce one in a non-stick burning smoker like a Cook Shack if you need that look.