Progress has been made! There was some embroidering in the evening, and during weekend free time, so here's some more proof:
As you can see, I've opted for the Bayeux kind of couched work - long stitches covering the ground, then long stitches across those, and the latter stitched down to hold everything in place. It was nice and quick to work, and I really enjoyed it.
It's far from perfect, but then, it's just some fancy mending after all!
And for those of you interested in that kind of thing, here's the back of the cat:
You can still see where the original hole was if you look closely!