Are your exhaust tips cut off at 90deg & pointing straight back? or are they angled downward slightly and cut off at an angle?
Dr. Dan Horton might be able to reference some research/ tests & or photos to illustrate what has been proven to reduce floorboard pulsation.
An SS skin on the bottom of the floorboard area would serve as a fire protection and properly done with a sandwich of vibration damping material, should calm and quiet things down.
I like the SS heel pads as described above for the inside.
I expect the F117 Engine nozzle theory might be useful to consider for your exhaust tips. Not so much for heat signature reduction , but for noise and vibration reduction.