I dont smoke chicken very often anymore and when I do I go skinless. Been spatchcocken them lately with alot of success and still get that smoke flavor. Way better then beer can which had been a mainstay for a long time.
That said, I dont think you were at 350 very often or very long because the skin should have crisped up at that temp. Below 275 makes a nasty chicken skin in my opinion. So how were you measuring the temp of the cooking chamber?
Pete-my first UDS,a brick pizza WFO, a leaky Chargriller offest, wifes Weber Genesis gasser,a Lightening Fast RED Thermapen, new baby Traeger