Here is some information about the Hanover Displays' flip dot board controller PCB: PCB 7080/02/01 ISSUE C.
The firmware runs on the main CPU of the board, IC2: Hitachi H8/323, and is stored on IC7: SST 29EE010 (1 Mbit EEPROM, PLCC32 package).
The factory firmware is compiled with IAR Systems H8 C/C++ compiler, but it is not publicly available software.
Suitable PLCC32 programmers for dumping and/or re-programming the firmware: