Hi John
All your chips seams to be supported so getting your board working shouldn't be to hard.
As fare as i can see on flashrom.org, the status for writing to "SST SST25VF040.REMS" is just unknown, if it really doesn't work, then another option might be to find a compatible chip that is supported for write. In any case you will probably need to desolder it so that you can switch back to the original in case your port doesn't work in the first attempt (likely).
I sugest that you copy the code for Kontron 986LCD-M/mITX, as it seams the closes working match. You might also take a peak at Tyan Tiger K8W (S2875) as it uses the same SuperIO as your board.
-Anders