So I've been doing some science (I use that term very loosely)
First thing in the morning, exhaust is quiet (aside from high idle) So quiet in fact, that sometimes it sounds like the stock exhaust is back on. As the exhaust heats up, it gets louder and louder, then eventually begins to have that boomy drone. I wonder if the exhaust is heating up and expanding enough to contact something under the car?
I'll report back.
Edit:// I was wrong.