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|One more thought: the cabin heater core can come loose on these cars. You can check by pushing and pulling on the pair of hoses going through the fire wall. Though I have no idea what this would sound like if it was vibrating.
This is probably not useful, but I was wondering if the sound is the same with the top up and down. When I put the top up on my car, it amplifies the low frequency exhaust noise rather annoyingly. But it does this all the time, not just when wared up.