I think one option would be to simply buy something that uses i2c or SPI.
Worst case scenario, if you won't be able to source your display after a few years, you could just program a tiny microcontroller as an inbetween your arduino and the new lcd display, to "translate" the commands the old lcd display required to the commands the new lcd display expects.
Actually, even with the 4bit/8bit parallel 40x4 numeric displays, you could just put a tiny microcontroller between it and your arduino, which would translate the commands received through i2c or spi, into the lcd display commands. A pic12f or pic16f with 10-16 pins is less than 1$ in quantity.