For your first attempt, that is outstanding. I know people who have been doing leatherwork for decades who couldn't do it that well. Nicely done!

I have to second Tyger's statement. There's a big difference between rubber cement and contact cement. We generally only use rubber cement for a light temporary bond before stitching something down, as it just doesn't have any 'holding power' by itself. Contact cement, though, is incredibly strong if applied properly to leather that's been surface-prepped for it.

You'll want to roughen the mating leather surfaces (don't be afraid to scratch it up like it just came from a chick fight!) before applying the contact cement. Put a thin layer on both sides, let it get tacky, and press them together.

If it were me, I'd also back it up by putting some small stitches through both pieces. They can be cleverly hidden in the recesses of your swivel cuts. Just a couple of stitches in various locations should do the trick.