"What am I overlooking?"
I don't I agree with your interpretation, as it is about the act more so than the experience; I do therefore I am. However, that is not really relevant as we are talking about starting points and in cogito ergo sum doubt is the stating point. At first all personal experience must be rejected to reach this truth, so even if you think the end results is about experience doubt is the starting point.
“Doubt is the beginning of wisdom.”—Aristotle
"But would you consider those to be epistemic starting points?"
I believe I already said that I do.
Thank you for the clarification! Doubt, curiosity, and reason are not generally considered to be "epistemic" starting points for knowledge as philosophers and most interested laypeople define "epistemic", but of course you're free to define your terms any way you want. And I do believe I see the sense in which you are stating that doubt, curiosity, and reason are starting points. I would agree with you that they are indeed starting points in that important sense.
I would disagree with you, however, that the sense in which you are making your claim has anything to do with the sense in which @Curious George was making his claim.