First, let me make sure of when this vibration occurs. Just in the burnout, correct? Not down track at all?
It's entirely possible, that at the fairly low rpm you burout, that it's trying to hookup, and is in fact wheelhop. The times it didn't vibrate, there may have been more water in the box.
How quick do you run? Any car under 12.00 should have enough power to do a high gear only burnout. Try starting in high and wind it up, say 6000 rpm or so for about 1.5-2 seconds then roll out......
JMO,
Johnny