Good evening Giles and welcome to the Events Calendar Support forum!
Thank you for reaching out to us.
We are sorry to hear about the email issues you are dealing with.
I would love to help you with this topic.
You can have the system send tickets from any chosen email address by simply installing, configuring and testing the following plugin: https://wordpress.org/plugins/easy-wp-smtp/
Using a real SMTP server with authentication will bypass the built-in WP mail functionality altogether.
Please make sure you configure and test the settings using the plugin’s built-in tool.
With that in mind, I am also noticing that you Event Tickets Plus version is far behind and would definitely benefit from an update.
That would make things work much smoother for sure.
Let me know how that goes.
Best regards,
Geoff B.