Well considering that you were off by a whole year, I imagine that the specific date of arrival is a little less significant. But if we can continue this line of thought then now that we have established that, lets return to the provisions that were allotted to Jefferson Davis in February 1861 when he sent the mission to the North.
If he had no legal precedent to send a legation to the North in 1861 since, as you said, he had no treaty making power, what reason would any of the Northern government have to listen to this group at all. I’m really looking for an opinion here since it would be impossible to say definitively why the individuals involved did not engage this commission.
By Lincoln’s own admission there were peace negotiations just before his first inauguration. The details are irrelevant because Jesus Christ himself would have been turned away by that blood thirsty goon President from Illinois.
Jefferson Davis did what he could within his powers to avert the forthcoming disaster. Lincoln did not. Lincoln could have brought them in and negotiated with them. There was nothing stopping Lincoln from doing so.