If you're dealing with a YEC, the TOE itself is probably not the place to start. The first thing I would start with is deep time, and as evidence, I would point to the stars. Just take them outside and point to the blurry patch that is the Andromeda Galaxy which is 2 million light years away. Without getting into details, that is really the simplest thing to show someone and it's very accessible and immediate.
For the TOE, I know you discounted biogeography, but that is also pretty straight-forward and easy to understand (marsupials, Darwin's finches, ring species).
For human evolution, I'm partial to Lucy. She's a hominid that is fully bipedal, but otherwise very chimp-like.
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