Where can I find a fast (1KHz) LCD plate?
What you're looking for sounds like an LCD shutter, specifically a Pi Cell LCD Shutter. The more modern welding helmets use the TN LCD Shutters which have the same slower speeds as 3D shutter glasses. From what I've read the Pi Cell LCD Shutters can have a switching speed of up to 1000Hz.

Liquid Crystal Technologies claim they'll send you a free 1"x1" or 4"x1.5" TN LCD shutter or a 1"x1.5" pi cell shutter. The pi cell shutter will be the faster one. I've never needed an LCD shutter, so I can't verify anything any company claims about theirs, but free is certainly worth a try if you can get them to send you one.