Once ignited, pellet grills are pretty basic, fuel feed and air supply.
250F is a good temp for a stable fire for sure, I would check the following;
1- Remove all pellets and vacuum out, look for crumbled pellets indicating moisture degradation. Be sure the auger is moving fresh clean pellets.
2- Fire Pot, deep clean, make sure all air entry holes in the sides are clear of any ash, and that the bottom is scraped clean of residue, especially around the hot rod ignitor. The fan pumps air around the auger (cooling it), around the firepot, and finally thu the holes and into the firepot to stoke the fire.
3- It wouldn't hurt to check under the hopper to make sure the fan inlet is clear of any insects etc.
Does the fan sound normal? I now do a quick vac of the firepot etc. fairly often to keep it running well, plus ash is corrosive so the less left lying around the better.
Hope that helps.
BTW, when I'm at 250F or higher, I see little smoke, and NEVER more smoke when shutting down. Sounds like poor air flow for some reason. Shutdown stops the auger, keeps the fan going, so remaining pellets burn up completely. Finally when done, it "burps" the auger to drop a few fresh pellets into the pot for the next ignition.