Lincoln and Butler were to meet, that is a documented fact. Butler wrote what was discussed in the meeting, just like many people wrote what they discussed in meetings with Lincoln. You yourself have quoted many of them, I'm sure. No one disputed what Butler wrote back then. Disputing the meeting is a recent invention of revisionists. There is no reason to doubt Butler, other than you just don't like what Lincoln said. Applying your "Butler standard" to the Lincoln legacy eliminates more than it preserves. Just think, you would erase more of Lincoln than Booth could ever have hoped to do.
You can't possibly prove that.
There is no proof that Butler even met with President Lincoln on the day in question.
Walt