HI,
Might it be as simple as putting a low leakage diode in series with the 5V to the LCD?
Keep in mind:
- The display would only get ~ 4.5 volts
- The leakage through the diode will drain the charge of the LCD so it might not stay dark when un powered as long as a mechanical switch.
I guess you could use a small relay.
Have you left the LCD "Valve" dark and un-powered for an extended period of time? I would think the charge would slowly dissipate but have no idea how long it would take (i.e. minutes, days etc).
Good luck.