Was Barth an experientialist?

Andrew Reid's notes for the Apologetics unit of the Moore College Correspondence course helpfully gives three broad distinct approaches to apologetics: presuppositionalism, evidentialism, experientialism. Practically, these respectively lead to an emphasis on proclamation, persuasion, or personal testimony.

I found it curious that Reid classifies Karl Barth as falling into the last category of experientialism. I think that on some level Barth has more common ground with approaches with an emphasis on proclamation. He had reservations about apologetics in general. There was no reason to not be confident about the truth of the gospel. Theology does not have to justify itself. He considered that theology had a role to play in the university (even in the secular public university) because it called into question the presuppositions of other academic disciplines. But there is great irony with classifying Barth as a presuppositionalist because that puts Barth in the same camp as Cornelius van Til, the doyen of presuppositionalism. He was one of Barth's harshest critics, diminishing Barth's influence in conservative North American circles.