I agree, these questions are part of the work that would be required to take it from a prototype to something useable.
You could maybe add one big transparent layer on top of the page which would catch all "real" clicks and generate synthetic mouse events under the layer at the stabilized position.
Browsers aren't an "ideal" environment (versus an OS where you might be able to hook into the mouse position/display at a lower level), but at the same time, they are ubiquitious, cross-platform, etc.
Might be worth a shot to expand this more. It's on my long list of side projects -- I'd love to collab with someone on it!