The Apple Super Serial Card uses address line A11 to switch the card's ROM to always to the same page ($700), when any part of the $C000 - $C7FF space is accessed. An access to $C800 - $CEFF is mapped to $000 - $600. This takes place in the first part of the CPU cycle, when the address bus becomes valid, so the ROM has enough time to react.
Why hadn't I thought of that myself? I mean, the guys at Apple only did that 40 years ago. But I am just a software engineer, to my own defense.
As soon as I got home yesterday, I made the modifications necessary to support the new address decoding for the EPROM. This required only the change of one line of VHDL code and the connection of A11 to a CPLD pin. I repurposed the unused /IRQ pin for that. Now I can access all pages of the ROM again!