That's OK, MHeadroom. You're about 5 days ahead of me already. My Dot isn't arriving until Monday.
Is the 82802 chip a 32-pin PLCC? If so, is there enough clear space around it for a socket? (I fixed a motherboard with misflashed BIOS (my own bad) last week by unsoldering the chip from the m/b, adding a socket, and flashing the chip in the EPROM programmer at work.)
I've done some more reading, and found that a compatible BIOS chip is the Atmel AT49LW040. Unfortunately, the EPROM programmer at work does not handle this chip. On the other hand, a flashing utility that handles the Atmel might also handle the 82802.
On the Linux side, there is a project called flash_rom that will flash 82802ab chips. I don't know if that would be applicable, since it appears to be aimed at doing embedded Linux.
BTW the datasheet for the 82802 chip is at http://www.intel.com/design/chipsets/datashts/29065804.pdf