No trust of northern politicians would have been needed. All the Southern states needed to do was indicate that the Corwin Amendment would be acceptable to them as the condition of their re-entry. Lincoln strong armed 5 states to ratify it. The Southern states after making it clear passage of the Corwin Amendment would satisfy them, could have just sat back and watched Lincoln strong arm more Northern states to ratify it. Once enough had done so, they could have all re-entered, ratified it and that would have been it. It would have been a constitutional amendment. They did not need to trust anybody. They could have just sat back and said "show me".
They didn't. They never gave the slightest indication that the Corwin Amendment would address their concerns. Because their real concerns were not about the protection of slavery.