Disassembling the Z80 ROM is probably the best way to go, but don't plan on cheap labor! I used to be pretty good with Z80, but it would still take me many days of effort, and I would want access to the hardware to check signals.
Given the major errors in (or out of date nature of) the documentation, there is no guarantee that the schematic you posted is correct.
You will need to explain the format of the bin file you posted.