Of course, the Confederacy was not going to stop their insurrection.
War was their chosen path, and slavery was their bottom line, as demonstrated in their final negotiations with Lincoln in early 1865.
Even at that late date, Confederates could not "broker a peace" if it meant ending slavery.
We should also mention, again, that peaceful secession was still possible in 1861, if Southern representatives in Washington had gone to Congress and/or the Supreme Court to achieve lawful, mutual consent to their disunion.
Such a path would have been difficult, time-consuming and would not provide the sense of urgency and unity as a nation which the Confederates felt necessary.
But it would have saved many lives.
Yes, eventually the peace was brokered by RE Lee and other surrendering generals.
What a shame that hundreds of thousands of potentially productive lives were cut short.
I think the big secret was Virginia, the most populous of the slave states would only join the insurrection if there was a war, and so the slave power started the war they needed to get Virginia in.
Certainly Virginia had no problem putting down an insurrection in Pennsylvania when RE Lee’s father was governor.