Try the high octane fuel -- it's a worthwhile test. But it's unlikely that's your problem. Your engine has a knock detector that retards the ignition if the engine begins to ping, and it would/should do so in this situation.

Look for a broken or loose heat shield on the exhaust pipe and/or catalytic converter. Also, one symptom of a failing cat is a rattle -- the fractured ceramic honeycomb starts to rattle.

You could also have a loose or broken bracket somewhere underhood.

Can you hear the rattle if you rev the engine, parked, hood open? Or must it be under load?
--
Don Foster (near Cape Cod, MA)