re: damping factor
the image you sent was at too low a resolution to make much out, but
a few things i've noticed is:
1) there is no output protection, or sense resistor for feedback
2) there is no damping at all across the yoke (it will have the
same gate-drain breakdown problems that the present design has
3) the voltage rating of the MOSFETS will have to be the sum of
the supply rails.
for a class AB driver, my cube neighbor suggested the LT1166 Power
Output Stage Automatic Bias System.