[Al Skierkiewicz]

Greg,
In looking at the upper curves, the PWM values make a change as soon as the gyro output decides it has gone past the target, so I don't think you have delay in that part of the system. i.e. no delay in the gyro, software or PWM output. As I remember, the Victor has an output frequency of 150 Hz (old ones were in the 2kHz range) so there could be some delay before an input change would make a change in the output but that still would only be 10-20 mSec. I still think you are dealing with mechanical motion. You mentioned in an earlier post that you are using a transmission and chain drive. I would think that you could easily calculate the delay in taking up the slack in a chain at the output RPM of the transmission and add that to the other known delays and see if you are getting any closer to the measured result.
The picture background reminded me of the Philmont area near Cimmarron, just east of Angel Fire.