Your first link shows:
Item One: Serve scaled images ... F High Priority:
Item Two: Specify image dementions ... F High Priority
Image on front page is 1.1 Megs. You are using HTML parameters to re-size to fit on
the Moodle screen in space desired, but that does NOT reduced the actual size of the image.
This makes servers/browsers work harder.
Change that alone and I'll be you see an improvement on the front page.
If there are other images that you've resized by grabbing the right corner and shoving in, reduced the size of those as well.
One could install an add on for FireFox called FireBug ... enables one to inspect elements of any page you can access ... including those one cannot see unless logged onto the site.
Where you have this hosted and the package purchased indicates a shared server and is limited (called it 'choked'):
mod_bwlimited/1.4
Hosting companies typically install the module to limit clients. They don't want clients to have much control over this module through htaccess.
Suggest contacting hosting provider help desk to see if they can provide some tricks for you to use.
'spirit of sharing', Ken