You say Draupadi's polyandry is "unexpected, devoid of precedents". It is unexpected to Drupada most particularly, since the Pandavas have been given to expect it by Vyasa a little while beforehand, and Draupadi herself takes to it very nicely. But there is apparently the precedent that Yudhishthira mentions. As you say, that the polyandry demands explanations -- and so it is given plenty of them. How are those explanations "unconvincing and weak"? In context they are strong enough to be convincing to all surprised parties, even if Karna later says she is a whore.
All the best, from Simon B.