highest damping factor amp

You don't need a high damping factor to control TAD woofers. My amp has a very low damping factor and works great with the dual TAD 15" woofers (1602s) in my system. Now they are in series for a 16 ohm load, so nearly anything can drive them. And they are very satisfying as they go to 20Hz in my system :)
If you wire them in parallel, **any** solid state amp that can make a few watts and many tube amps will drive them just fine.

Now if you over damp them by using an amplifier with a very high damping factor, you'll actually get less bass and no definition. There aren't any speakers out there that really need more than about 20:1 damping factor. IOW, the damping factor thing is a bit over-rated. What you really need is the amp's ability to make power, and with the efficiency of the TADs, that really isn't all that hard.

check this
http://www.bcae1.com/dampfact.htm
 i myself use crown k2

df 3000
wire length 3 ft
wire awg 2/0

damping result 2711the k2 is now installed on the subs side with the terminals close to the driver terminals

Back EMF causes current flow in opposite direction to one that would cause motion of the membrane in given direction.  This current will produce force moving membrane in opposite direction - braking movement completely, like shorted motor.  Except, it is not completely shorted - voice coil impedance is in series with it.

Resistive impedance of the speaker's voice coil is about 2/3 of the rated impedance.  Since this resistance is in series with the back EMF it will reduce overall damping factor to 1.5 max.  We don't want to make it much worse than that, but DF=15 amp would make it only 10% worse.

DF specification might be important for other reasons but for the reason of the damping is pretty much useless.