Looking at the headers that were used on your tests and those rules I don’t see any that should have been triggered either. I certainly wouldn’t recommend giving up because it’s a pretty big performance deal (close to a second if not more) and if it really is being caused by their base install it’s happening to all of their customers on the shared hosting.
Is there any way to stand up a simple test page that is just a straight static html page with a few images (and no .htaccess) in a top-level directory somewhere for testing?
Honestly, if you can prove it is from their config, their engineers should be working to figure it our and if there are any forums or discussion groups it would be worth checking to see if other customers are seeing it and to get more pressure applied.
Worst case I’d recommend switching providers - you shouldn’t have to go with a VPS plan to get reasonable shared hosting (webpagetest.org is on Dreamhost shared hosting for example and they do not have the same problem).