Lots of recommendations to check seals, gaskets, etc. Now, I don't run a pellet stove, so I may just not understand the problem, however how can a bad gasket cause a CO leak? Isn't a properly installed pellet stove under constant negative pressure, like a wood stove? Chimney creates draft, which creates draw. Any leak will cause room air to get sucked into stove, and cause stove to overfire, not allow CO to leak out. If you have CO leaking out, you have a draft problem, not just a gasket problem.
As I see it, either something is preventing proper draw of the chimney (poorly configured chimney cap, wind, kink in the liner, etc.), or draw of pellet stove is causing some other appliance to back-draft, or some other appliance is causing stove to back-draft. Since it seems to be present in the stove room, I would see if the same problem occurs when I shut down all other drafting appliances (clothes dryer, kitchen range hood, water heater, furnace, etc.). Are you running any of these appliances when the problem occurs? Does the draft on your stove seem particularly weak?
Again, FD or gas co can bring in a better CO detector, which may help you identify the source of the problem much more quickly.