1) Most versions of DOS boot floppies can create a RAM disk from main memory. Install some of the files there to free up room on the bios data file disk. This is what the latter DOS boot floppies did to get extra space.
2) Install the bios data file on your C: drive root. Create a small FAT partition to hold the file if you can't read the C: from DOS.
3) There are USB installs for DOS on thumb drives if the MB supports boot from USB.
4) Flash from Windows, it seems to work fine these days, at least on XP.
Are you sure you got the right Bios file? I can't beleive ABIT made that big of a mistake. Though Plextor did once on a DVD firmware.