You could make the basket on a post with a small overhang that can wedge your "discs" in it. They could potentially bounce off too if you're too aggressive.
Or you could put a little fake basket on a 1/4" dowel, and play the old pole hole rules: if it touches the pole, it's "in." But that would be a much larger target than your current hole. Unless you made the discs smaller, of course, but they're already pretty small.
In reality, I don't know that you could improve upon what you've done.
How long does it take to tear down and set up another hole?