I've made some progress, sifting through old forum posts and broken links.
The flash memory (IC 11) has its enable pin controlled by a CPLD (IC 16), which I've read has sometimes needed a reprogram with the s3esk_cpld_design.zip - originally from Xilinx. However, this is no longer available on Xilinx's website - though through the magic of the WayBackMachine, I've managed to download this zip (and others) for safekeeping. I will try to upload the cpld example and report back with my results.
If it is ok, I have attached the zip here as it should be better indexed for future users to find, rather than on wayback machine. If this is not allowed let me know and I will remove it.
EDIT: Yes - it works! I used impact to program the .jed file in that cpld example zip to the cpld (xc2c64a). Before I did this, I asked for checksum from the cpld and it came back different. After uploading the example the fpga works from the flash without problem.