Ah, that more detailed explanation explains it. From the sounds of things with a partial load the wood is not burning all the way with 80-90% air. I suspect this will not happen with a fully loaded stove, at least that is the hypothesis.
How are you loading, N/S or E/W? At the end of the burn cycle is the wood burning down completely to ash?
Can you try loading the 5-6 splits, N/S, before lighting? Load it with three, 4-5" splits on the bottom, then 2 more on them. Like a truncated pyramid. Then make some newspaper knots and put them on top of the wood and add kindling on top. This is also known as a top down start. See if that improves the smoke issue.
Top-down lighting -