Stephens may just have had an incentive to "spin" what happened at the conference. All reports I have read, with the exception of those quite obviously trying to be Confederate apologists, agree that Lincoln's terms were: reunion, acceptance of emancipation, immediate cessation of hostilities, and the disbanding of all Confederate forces.
Some differ on exactly what was meant by "acceptance of emancipation," but I have noticed that the pro-Confederate sites tend to leave this plank out entirely, making it logical to assume that their story on other issues may be less than complete.
The only reports you will read are from, or based on the accounts of, the men that were there....none of which will be purely objective. You suggest in post #7 that the Confederate representatives demanded the continuation of slavery (one of Lincoln's demands "in reverse")...yet no accounts, from any side, indicate that the Confederacy was demanding anything other than independence. One need not be a "Confederate apologist" to understand that Lincoln full well understood that slavery was a dying institution...the secession of the southern states would have expedited this. Lincoln himself stated this...Lincoln advocates like Harry Jaffa have stated this...Professor Jeffrey Hummel laid out a lengthy economic analysis in his book Freeing Slaves, Enslaving Free Men that confirms this. We should take Lincoln at his word that the war was waged to prevent the southern states from seceding...not to end slavery per se...and, again...the question is why? What moral or Constitutional authority did the federal government or the union states have to force the southern states to submit?