Stroke Taper Improvements

I'm often using stroked shape paths for my 2D motion graphics and illustration work.  I like the idea of the Taper settings, but I feel they are very limiting.  Can we have something similar to the Feather tool to change the width of a stroke manually?

And/Or, could you add some more settings under Taper, like:
Middle Width
Middle Offset (% of length of path, to move where you want this point to be, not locked to 50%)

This might negate the "Start Length" and "End Length" properties, but not sure.

Also, can we adjust how the Start and End Ease are calculated? 

Currently if you have your Start Length set to 50% and no easing, you get a sharp change of width in the middle (see 1st image).
Increasing Start Ease to 100% makes this transition in the middle smoother, but also majorly fattens (and flattens) the start and gives it a weird 'elephant's foot' effect (see 2nd image).

Maybe there's sort of an "Easy-Ease" option that eases the taper in and out?  I would like it to look like the 3rd image mockup.