I reckon it is most likely a part of your exhaust hitting on something. Sounds like the engine is torqueing over just enough for the exhaust to make contact with something.
You indicated you
had the exhaust parts installed. I'd suggest that you take it back to the installer and ask them to check it out.
Bubby says to get it up on a rack and take a crowbar and push over any part of the exhaust that even looks like it might touch something else ......
humfrz