The King of Saxony was Duke of Warsaw in this TLL just like OTL, but Napoleon did not allow him to be King of Poland because it would hinder his plans to create a guard dog in central Eastern Europe.
Napoleon chose Davout because he has the ability to follow his orders to the letter while maintaining his individual initiative and his iron discipline is extremely necessary in this case. Davout is the type of person who, despite being King, would continue to serve Napoleon without questioning. Bernadotte rejected the same year an indirect proposal to be King of Spain so Napoleon cannot be very sure about whether he would comply with his orders diligently. Although it is an interesting scenario anyway and I am forced to think about it.
Having the Duke of Warsaw AND the King of Poland seems to be excessive and situation when the Duke of Warsaw is also a King of Saxony (and in his Ducal capacity is subordinated to the King of Poland) does not make sense. The issue of “a guard dog” is irrelevant because neither OTL Duchy nor your Kingdom would be allowed any true independence. What would be needed is a reasonably prosperous and loyal state capable of raising big number of troops and supplies.
Now, as far as your argument regarding Davout is involved, it is not very convincing. Being loyal and maintaining discipline within an army corps is not the same as being a capable administrator on state level and while it can be argued that Poland needed “discipline” a person who would try to enforce it was not going to be popular. And if Nappy wanted to maintain Poland loyal to him candidate with a proven tendency to alienate people is not a very good one especially if you add a complete absence of any experience in the civic administration, diplomacy and any other relevant area including raising and supplying an army. The Poles needed someone capable of charming people into doing what is needed rather than a severe martinet issuing the orders.
As far as Bernadotte was involved, his loyalty had to be bought but he already proved that he can manage a big foreign territory without generating any unhappiness among the locals which was rather rare (city council of Lubeck presented him with 6 horses as a token of appreciation of him stopping the looting after city was stormed; in Hanseatic towns he became quite popular as a governor, when he was in charge of the French troops in Denmark he, again, became quite popular and even was awarded Order of the Elephant, after Walchern he accepted the general government of the Roman states). His acceptance of a specific position could not be taken for granted because he tended to use his brains (as was the case with Spain) but in your TL Poland Nappy would need somebody capable of acting with a great degree of independence (unlike OTL Duchy of Warsaw, this would be a big state with a complicated internal and international situation). Prior to the acceptance of the Swedish offer there is no reason to suspect any disloyalty and even as a heir to the Swedish throne he went on the other side only after Napoleon’s openly hostile actions.