The theme creators also argue that going https (ssl) could be causing speed issues - do you think that is valid?
To a small extent, yes. HTTPS is not cached by the browser, so every time the browser visits the page, it needs to load, it can't just pull a previous "copy" from its cache.
However, that's more like a 1 to 3 millisecond difference, not 80 seconds.
if it were the theme and plugins slowing it down, it would still not cause a 'failed to connect with server' error or timed out.
Yeah, I still think it's a server issue, but the only way to be sure is to rule-out the theme and plugins.
I am trying to find some evidence to rule out the theme and plugin so I can go back to GoDaddy and say, look it is not the theme and plugin because
That's exactly what this test will give you. ;)