Is "with" necessary here? Because it seems fine just with "even."
Native speaker’s answer
Rebecca
"Even with" in this case is used as a variation of "though" or "even though". It is used to mean "despite the fact". You could replace "even with" with just "even" here, although it would not carry out as strong of a meaning and it would sound a little less natural, since "even" by itself doesn't quite mean "despite".