After a few (actually many) attempts, I can finally write to the EEPROM (AT28C64E) in a reliable way. It took some additional reading, reverse engineering and finding other’s schematics and sources.
I also got some help from Henry S. Courbis from ReactiveMicro.com/UltimateApple2.com. He pointed me to the right way to create the /CFFF latch. I used a 74LS74 flip-flop for the Set-Reset circuit, but had the D and Clk pins bound to ground, as I found it in numerous schematics.
Henry pointed me to the fact that he had to pull the D and Clk high. This actually did it and I can write now to the EEPROM to corresponding page, for the slot the card is in.
Next step was to fully decode the $CFFF address using a 74HCT 133.
This allowed me to read/write to/from the $C800-$CFFE ROM address range.
Next I found that the EEPROMs I ordered through AliExpress are counterfeit/defective. Writing to some addresses resulted in errors when verifying. This meant I had to order some other EEPROMS. Unfortunately the 28C64E aren’t produced anymore, so I had to settle with the 28C64B, which have a slightly slower write timing.
I ordered some PCBs and SMD parts, which I already have received. I soldered one card and programmed the EEPROM. I can say it is a success. (Although I had to cut two traces and lay some wires).
Next step is to implement /DEVSEL.