Here's another thought and a slight modification on your idea, if you don't mind:

Search for some of the wrap jobs cudak888 does on his bikes. He is very good at reverse wrapping, i.e. starting at the top next to the stem and working your way to the bar end.

When I've tried this, I'm challenged to find a clean way to finish the end. A sleeve similar to what you've done would be perfect! I'm not certain how to fit it to various thicknesses of bar tape, but a clever genius like you, should have no problem with this challenge.