This is not feasible. Worth an idea, I think.
After extensive back and forth with support, I found out that there is a way to change the from email address for Sales Insight emails, and all you have to do is add an "email" field to the User record in Salesforce, then update the settings as indicated above to select the other email field on the User record.
Users could update the secondary email to whatever they would like, however, the From Name that populates on an email is still pulling the first and last name of the User, and Marketo doesn't have a work around for that. In our case, where we would like to enable admin assistants to send out Sales Insight emails on behalf of the salespeople they support, this would not work because they could change the actual email address, but their own first and last name would still pull into the email.