I made two small additions to my OEM tool kit that will allow me to take the seat off using same:
First, a trip to Harbor Freight for some socket caps (I used the middle one for my tool):
Then I rummaged around and found a cheapo 3/8" drive 10mm socket. Here are the components of the tool I made (the article on the right is the 12mm "socket" from the OEM tool kit):
Here is what everything looks like put together (I use the screwdriver bit from the OEM toolkit as a "T-Handle" for the 12mm socket):
The additional parts (the 3/8" drive socket cap and the 10mm socket) fit easily into the OEM toolkit bag, along with the rest of the tools.
Works for me!