To update this, I’ve tried using both SendGrid’s API and SMTP without luck. I’m authenticating via API key, and verify the settings using the form within this plugin’s Settings page.
We can take Contact Form 7 out of the picture, because just normal “Forgot my Password” emails generated by WordPress itself do not get sent using SendGrid even though it is set up and configured.
I’m hosting on Pantheon, so this is really important – email is undeliverable unless sent through a third party transactional service. Perhaps its an issue with the latest version of this plugin?