After spending all day trying to get something working, I’d like to request that the plugin author consider adding support for the SendRawEmail function and sending attachments. I tried using this code as a replacement for most of the plugin code: https://github.com/daniel-zahariev/php-aws-ses
However, while I got emails working again, I am still not getting attachments. Without attachments, this plugin has very limited functionality since, as the OP noted, Contact Form 7 is made to handle this sort of thing.
