I went with the GIGABYTE WI07HT from Oxfordtec, because the WI01GT was sold out.
Installing the card was as simple as unscrewing a couple of little phillips screws, and popping out the antenas, placing the new card in and popping the antenas and screws back into place.

After installing the hardware, I booted up my eee, whihc is running Ubuntu-eee, only to be greeted with kernal errors:

CPU#0 stuck for 11s

OHNOES!

I tested my BT3 usb thumbdrive, the wifi works fine in here (which is a positive, because BT3 didn’t like the RaLink card at all!), so I knew it wasn’t a hardware issue.
Of course I had wifi drivers coming out of my ears after I’d installed madiwifi, madwifi-ng, and a karma-patched madwifi. None of which did me any good.

Disabling Wifi in the BIOS menus is the only way I could boot back into Ubuntu eee. This lead me to the idea of checking for BIOS updates.
It turns out Flashing the BIOS to the latest version ended up fixing the problem.

Create a FAT32 bootable USB disc (using HP’s Disc Util), and Windows ME DOS files (98 DOS files do not work).

Then just copy AFUDOS and the latest firmware ROM onto the disc, and boot from it (Hold ESC during eee’s startup for the option to boot USB).
The command is;

afudos /i1111.rom /obackup.rom

Where 1111 is the number of your new firmware. This will also backup your old firmware to a rom called backup.rom.

You can download all the tools (AFUDOS, HP Disc Util, DOS files). And your latest BIOS firmwares here.