Here is the toolkit of work-arounds I have found and use.
I invite your comments and additions to the same. The last
paragraph indicates a satisfactory 'final' state for me.

1...If the video problem still leaves you some modicum of control,
for example if your problem is missing frames on windows,
or if the only problem is that windows can't remember
to come up un-maximized, and BEFORE going to step two,
try the following:
a. unplug & replug mouse's nano; and/or
b. LXDE Menu item Preferences/(Re-) start ... Compiz; and/or
c. LXDE Menu item Preferences/Compiz...Mgr/Category Utility/,
for any fixes appropriate to your hardware.

2...If step one didn't solve your problem, or If your problem
is more serious as in an unresponsive keyboard, and/or
a cpu has gone into overload, then first try 2a, then 2b...
a. if lxpanel is set to hide-when-not-in-use, cancel GUI choice
immediately prior to hwniu, per LXDE bug report. If 2a fails,
b. ctrl-alt-backspace to reset X and re-gain control; likely not
100% successful, and work in progress may-be, and if using
Network Manager, wi-fi connection will-be lost.
If this doesn't work, then
c. reboot; likely 100% successful, but same hazards as in 2b.

3...For a more permanent fix, consider giving up on some complexity:
a. add no3d to /mnt-system/boot/syslog/syslog.cfg to disable Compiz.
b. uncheck the lxpanel hiding option.

After using Knoppix 6.4.4 for a while with no3d, I find about the
only video problem that occasionally turns up is with the lxpanel set
with the hide-when-not-in-use option. Now, usually solved with 2a.
I've not needed 2b since making the 2a modification in the GUI.
A big PLUS in the no3d case is an enormous improvement in apparent
responsiveness of the system to keyboard and/or GUI commands.