I have also an another LCD. The same size and controller LCD-AG-128064H-FHW K/W-E6 PBF
http://www.artronic.pl/o_produkcie.php?id=668?. It has the same symptoms.
The negative voltage is floating in mV range (~25mV) from -3.102 to -3.077 (from one line to full lines with "X")
Is something strange when two different LCDs behave the same.
I have tried:
1. Bigger, and lower pot resistances (from 1k to 20k)
2. Another negative voltage from MAX232
3. Separate the negative voltage with OPAMP (LM243)
The voltage float is lover (2 and 3) but contrast is not stable.