I have to do the same thing, but since the company I'm writting the addin for is using a version of Windows/MSOffice where the webview that the addin runs inside is handled by a IE11 process, I got OOM-error when trying to download an attachment bigger than 7MB via a EWS request (using the ews-javascript-api).
Now I'm using a IIS server to which I send the eschangeToken and EmailId and handle the download/upload of the email there via EWS-managed-api from MS.
Downloading the email as .MSG is not possible AFAIK, I download them by getting the MIME-content of the email and saving it as an .EML file.
Here MS provides some examples on how to use the ews-managed-api.