Why would anyone want to Analogwrite to the contrast pin?
A 470R resistor would be simpler. A potentiometer if you want something more complex.
I doubt if the rest of the LCD wiring appreciates having sharp edged pulses on the contrast pin. An RC low-pass filter would be kinder.
I bet that improving the electrical environment would solve your problems.
Mind you, your intententional text looks like gobbledygook to me.
David.