I just finished installing the GIVI T444 on my Cannonball bike (the Plan B version of my bike, that is).
The T444 normally uses a nylon web strap to secure the bag to the tunnel by wrapping around the underside of the bike. I didn't like that solution, and anyway the strap wasn't quite long enough to fit all the way around the GTS, and would have interfered with foot position. I could have gotten a longer strap, but I decided for Cannonball I would take a different route.
So I drilled some holes in the bag and secured it to the battery cover, using fender washers to keep it from tearing out. There are two upsized sheet metal screws that go into the stock screw locations on the front of the battery cover, and one screw toward the back of the bag in the center, which screws directly into a (new) hole in the battery cover. It's very secure.
The bag has very nice fit and finish. It feels like a good, solid bag. The main compartment is cavernous, and there are two narrow side compartments as well. The zippers are beefy, and velcro holds down the front flap of the main compartment. There is a generous amount of reflective piping on the bag as well.
The bag does not have a mechanism by which it can be locked, so during Cannonball I will be keeping the important contents (tools, mostly) in a reusable nylon grocery bag. This way, I can lift out the entire contents and take them into my hotel room at night. I could probably figure out a way to lock it if I thought about it hard enough, but at this point I'm pooped and can't take on any new projects.
I'm actually really excited about this bag. It gives me a significant amount of extra storage, does not impact my leg room, does not drag in the wind, and is reachable while riding. Plus, I can keep a hydration pack in there along with my tools. Big pluses all around.