Including error bands on the plots unfortunately makes them extremely busy and difficult to interpret. The regions of a colormap that are particularly problematic can be seen as dips in the weighted average (except for linear colormaps, where problematic areas are deviations from the "V" shape).
I agree that CAM02-UCS is not necessarily accurate over "long distances." I'm also not completely convinced that using color vision deficiency simulation to shift colors and then using CAM02-UCS to estimate perceptual distance is all that accurate either, but it's the best approach using currently published models. It's my understanding that modern color appearance models were developed using matching experiments, e.g., asking a subject whether or not two colors are the same; for "long distances," it would probably be better to show two color pairs and ask which pair is more similar. If you're interested in how such appearance models have been developed, I'd recommend [1], which is fairly comprehensive (but also quite long).
By my metric and others, I agree that Turbo is certainly better than Jet. For normal color vision, the metric I developed is fairly flat across the colormap for Turbo, which is close to optimal as far as rainbow colormaps are concerned.
[1] Fairchild, Mark D. Color appearance models. John Wiley & Sons, 2013.