Ok, I have a copy of the website on another server which is not live. I deactivated all plugins and enabled the default theme and it is the same, although a little faster due to having no plugins active. So the Admin message box loads in about 2 seconds and the user message box loads in just under 5 seconds. I have attached the latest query monitor screenshot.
I assume you can do everything you need to on the test site which is not connected by DNS? I will send the IP address and the FTP account details. There are other live sites on the same server though.