It looks to be a server problem. Chrome Dev Tools’ Network panel shows that the biggest slow-down is the
home_test.php page, which on my computer took 5 seconds (proof) from a cacheless refresh until the DOMContentLoaded event was fired.
If I were you, I’d take the index.html page and its assets (on a Mac, you can save everything by pressing Cmd+S), then upload that lot to another server or put it all on GitHub temporarily if you don’t have another server spare.
This will tell you definitively if there’s a problem with the server, or your JS and stuff. It doesn’t seem to be anything front-end, though…