I'm first language English and "Even I don't know how to answer that" doesn't sound correct to me for emphasis. It sounds like you're implying you're some kind

I'm first language English and "Even I don't know how to answer that" doesn't sound correct to me for emphasis. It sounds like you're implying you're some kind of expert who should know, and showing surprise that "even I" don't know how to answer that. If I wanted to emphasize, I would write "I don't even know how to answer that".