I have looked a bit at your old thread:
https://www.hearth.com/talk/threads/looking-for-a-new-stove-for-next-winter.105281/
In there you complain about a lot of coals in the morning. A few things are still unclear to me. There you say you split the wood 2 years ago but stacked it just the summer before. If that has been sitting in a big heap in your yard most of the time only the outer layer will be dry, the rest will still be wet. You may need a moisture meter to confirm if it is truly seasoned. (e. g.
http://www.harborfreight.com/digital-mini-moisture-meter-67143.html) Are those truly splits or just logs with a smaller diameter (aka larger branches)? Those need much longer to season IMHO. You also say you burn softwood; has that been split and stacked for a year?
You say the chimney is lined. Just to make sure: You do not mean a tile liner but a 6-inch chimney liner like that here?
(broken image removed)
You also said you have an OAK (outside air kit) but your house is very drafty. Why the OAK then? Have you checked that it is free of obstructions?
Then your stove temps; have you tried to get it higher than 500 F? How long does it stay there? Do you see the secondaries in the top of the firebox doing most of the burn? How is your glass; does that stay clean? At which temp do you start to turn down the air? When do you close it most/all the way for an overnight burn? When you have the air open but the door closed how does the fire look? Is it going pretty vigorously or are the flames lazy with lots of smoke?
Lastly, have you checked if your door seals right especially if it is warped? Take a dollar bill, put it between door and stove, close the door and try to pull it out. If the seal is good you should not/barely be able to pull the bill out. Try all sides/corners of your door.
P.S. Could you post some pictures? Sometimes that makes it easier to figure out what is going on.