The nice thing about deciding on a distance metric is that it gives you both a path (geodesics) and the speed, and if you trust your distance metric it should be perceptually constant velocity. I agree it's non-euclidean, I think the hyperbolic geometry description works pretty well (and has the advantage of well-studied geodesics).

I did finally find the duration logic when I was trying to recreate the path, I made this shader to try to compare: https://www.shadertoy.com/view/l3KBRd