NN with 1 hidden layer: Number of half planes visualised
A nice experiment!  I think you've just forgotten to include the final neuron's bias term.
As to the original approach, I think you're right that the hidden layer's output will be piecewise linear with 7 regions.  But after the activation at the final neuron you can cut each of those regions into two based on sign.  Plotting more of a heatmap for the actual outputs might be worthwhile.