I'll answer my own question since I was able to figure this out.
On older, non Matchmatic C3s, there is a screw that is visible in the center of the dial that holds the dial in place. On the Matchmatic, there is a round metal disc that covers this screw. Since the round metal disc has the printed numbers on it for the "scenes" and that was what I was trying to replace, I didnt want to do anything that could damage that disc, so I had to figure out a different way to get the disc off.
This is hard to explain, but I have two Matchmatics and I was able to do it on both, so I think it should be a repeatable process for others.
The first step is to completely remove the face of the camera.
When you have the face off, look behind the scene dial, and you'll see a round "cam" that is what determines the shutter speed. Through the center of this cam is the tip of the screw holding the dial in place. Using needle nose pliers, there is just enough of the tip of the screw sticking through that you can get a grip on the screw and with your fingers, turn the dial "lefty loosey" and it will start to loosen.
It takes a little bit if finagling, and your grip with the pliers will be harder and harder to maintain as you loosen the screw, but if you keep at it, you'll eventually be able to loosen the screw enough that the entire dial will come off.
Putting it back together is tricky though, since there is no way to stablize the screw to keep it from wobbling around as you try to thread it back onto the cam. There is a very thin brass washer in between the cam and the actual faceplate, so make sure you do not lose this washer.
Initially I was not able to get the screw to grip the threaded hole in the cam because every time I tried, it would wobble.
I ended up taking some wooden toothpicks and I jammed the tip of the toothpick in between the threads of the screw and the cam itself. This kept the screw in place while I was trying to thread it back on.
I know this is probably hard to visualize without having one in front of you, but if you are doing this yourself, if you have the parts in front of you, it should all be pretty straightforward.
It took a lot of trial and error, and probably on the 50th time, I got the screw to catch the threads in the center of the cam. Once you have it caught, you can just tighten the screw with your needlenose pliers.
One other word of caution, when you put the actual dial into position, there is a notched key on the back of the dial that positions it where it needs to be. For whatever reason, this camera was designed to where you can put the dial on either perfect or 180 degrees off. When you are threading the screw, pay attention to where the dial is and make sure its not off by 180 degrees.
Assuming thats not the case, get the tip of the screw to stick out through the hole in the cam and tighten it back up and you're done.
Its a pain in the butt to do, but like I said, I was able to do this on two different Matchmatics, so Im sure others can do it too.
If you don't care about the condition of the disc on the outside face of the dial, a much easier way would be to peel the disc off, and then you'd have direct access to the screw head and you wouldn't need to do any of this.
I couldn't see any way to get the disc off without destroying (or at least severely mangling it), and since I doubt it would be easy to find a replacement, I do not recommend this method.