Not sure if this was a bot or if they didn't care enough to bump their thread but I'll post this anyway in case someone stumbles into the thread from elsewhere:
Have a way to launch elf files (ie. FreeMC Boot)
Download PS2Ident
Extract everything to a flash drive
Run uLaunch
Navigate to where you extracted the files, ie. Mass:\PS2ident, and run PS2Ident
Wait a few moments and press start to dump your BIOS once the prompt appears on the bottom of the screen
You'll be given a selection of devices to save the BIOS to, choose your flash drive
Wait while the BIOS dump, it's a slow process
Exit the program by pressing circle once the BIOS finish dumping
Once you've done all that there should be a new folder on the root of your flash drive that contains that system's BIOS.