I really wish I had searched the forum for 'exhaust jingle' rather than 'exhaust rattle' as then I would have found this thread and not had to live with *the* most annoying noise for 6 months!
Just like the OP I initially though it was the exhaust manifold but couldn't hear any noise when I took it off. Since then I've swapped the power steering pump, tensioner, air con pump, had the gearbox off to check the clutch and flywheel (as well as all the heat shields and that).
But it just kept getting worse!
Eventually I found this thread and thought I'd add something for everyone else that will have this problem with the HKS 4-1.
Here's a pic of the exhaust chopped in half:
And here is the view inside the exhaust where you can clearly see the plate has come away from its welds:
Anyway is off to be TIG welded now so hopefully it'll be nice and quiet when back on (until the next thing happens!)