New Mouse

Try this

http://tf2.gamebanana.com/scripts/5771

Does that script go in a mouse?

Just assign it to one of the buttons on the CM Storm using a Macro recording of turning through 180º
http://www.coolermaster.com/cmstorm_files/Sentinel_Advance_II_Manual.pdf

See also setting in in Windows while you still have the Sidewinder driver installed
http://www.microsoft.com/hardware/en-gb/help/windows-8/how-to/mouse/calibrate-qt-mouse

MASQUERAID, It lets me record mouse clicks and keyboard taps, but don't think it lets me record mouse movements. The sidewinder does the quick turn fine.

Any other ideas?

All the Sidewinder is doing is sending a yaw instruction as a keypress, so why not add a macro to the Sentinel

TF2 has a function variable "cl_yawspeed" which is the speed your character turns on screen
In game it's probably set around 200 - think strafing speed
if you go for this x10 and then add a left or right keypress you'll turn x10 faster
You then need to add a delay which keeps the keypress working until you've rotated 180°
That's something you'll need to calculate in game

So your macro will look something like:

cl_yawspeed 2000;+left;wait 17;-left;cl_yawspeed 200

Select allOpen in new window

cl_yawspeed 2000; - increase rotation speed x10
+left; - send left button key-press
wait 17; - hold down key time in mS
-left; - send release left key
cl_yawspeed 200 - reset yaw speed once you've turned around (otherwise you'll be uncontrollable!)

Then either bind that to an unused key or use it as a script on the mouse

Is this all I use?

cl_yawspeed 2000;+left;wait 17;-left;cl_yawspeed 200

Do you know where I put it?