If – as we suspect – this is mainly a matter of shared hosting then I am not sure why you feel we should be able to solve it…

And while we can advise on the use of compressed scripts (which SP scripts are) and compressed CSS (which you can turn on in the forum options) neither of these are loaded on any other page than the one the forum uses so I am unsure how that would help although it can help load the forum page more efficiently.

The same goes for WP theme and other plugins loading components from third party servers and services. What can we possibly do about that?

All those things that you say Hostgator suggested are not within the province of Simple:Press.