I have been trying to fix this for a long time, and finally stumbled upon the solution!!

To change the e-mail address shown in the e-signature requests, you need to log into your Docusign account linked to the 'incorrect' email address.  Then go to Manage Profile in settings, and update to the correct email address. 

There was a bit of a verification loop to go through, but it updated rather quickly.  I sent a test e-signature request to myself, and it included the correct/updated email address.  The content of my e-signature dashboard in ProSeries was not impacted, all pending and completed documents are still there.