To successfully convert between two systems (or emulate one system on another system) it is necessary to have a very good understanding of both systems. That is my experience from having written software emulators. I have never built a hardware emulator.

Alphanumeric display output is actually fair simple. Numeric displays contain 7 segments and the dot/comma (for a total of 8 elements). Alphanumeric displays contain 14 segments, the dot and comma (for a total of 16 segments). The display board consists of 16 individual displays on the top and 16 individual displays on the bottom. That correspond to 32 displays. The individual top and bottom displays are controlled simultaneously as a strobe. The configuration for the top and bottom segments is set and then strobed. The next configuration is then strobed and so on until all 16 top and bottom configurations are strobed. It then cycles back to the first strobe. It's somewhat like how the old cathode ray tubes refresh their images. The image does not flick due to the way the human eye perceives the light even though the electronics responds immediately.

To build a converter you would need to understand how this works and importantly the timing because the signal is constantly changing. It would need to store the entire image for one complete cycle (from strobe 1 to strobe 16) and then construct that image to display on the LCD.

Note that Williams changed the on and off state of the configuration from the double (7) alphanumeric + double (7) numeric display (such as Swords of Fury) to the double alphanumeric panel (such as Black Knight 2000). The Data East on/off state remained the same for all their boards.

The status (credit/match/ball-in-play) is strobe 1 and strobe 9. Strobes 2-8 form the left of 7 alphanumeric and numeric and 10-16 form the right of the 7 alphanumeric and numeric displays.

The jackpot (extra display on Taxi, Police Force and River Boat Gambler) is done by taking away 8 segments from the 16 segments. This results in 8 segments available for the lower display (only capable of displaying digits) and the jackpot uses the other 8 segments (also only capable of displaying digits). The first (single) jackpot display uses strobes 2-8 and the second display (on River Boat Gambler) uses strobes 10-16. They are both only 7 numeric displays.

System 7 and System 9 is only capable of displaying digits. The digits are encoded using BCD (binary coded decimal). It's essentially a hexadecimal digit (4 bits). There is a decoding IC (4543 or 4558) that takes the 4 bit input and outputs the digit segment configuration for use in a 7-segment digit display. There are two BCD digits (upper and lower) for a total of 8 bits of data.