You are neglecting the first rule of diplomacy. In negotiations practically everything is on the table no matter how adamant one side or the other is about a given position. That doesn't mean a side will cave, but it does mean that there is always room to work. Applying your horrendous illogic, one could similarly say that by Lincoln's declarations that secession would not be permitted, the confederates had no reason to seek out a meeting with him for negotiation. Yet they did because they, being wiser than Lincoln, saw it a worthiable aim to at least attempt peace.
Along the same lines as your claim that the southerners would fairly compensate for property already seized Not at all. They had the papers and expressed every intention of paying.
a claim not included in the mandate approved by the confederate congress BTW.
Your timeline is out of order. The confederate congress did not even exist yet when the first team of negotiators arrived in Washington with sanction from their states to negotiate payment.
The second rule is to follow instructions. According to the instructions approved by the confederate congress, the men sent by the Davis regime had no power to negotiate anything but recognition of the legitimacy of the southern rebellion. They had no room to work. If Lincoln had suggested that the question of ending the rebellion and returning as states then the group would have gone home. Since that was off the table then, again, what was there to negotiate?
They had the papers and expressed every intention of paying.
Nonsense. Their instructions said nothing about paying for anything. Just vague suggestions about amicable solutions.