Is this something like the look you're going for? (You can adjust the style, transparency, etc). Q1_ac.mw
If you don't need the solid boundary of the leading side (that moves) then it's a great deal simpler to do. I just prefer this look. I find that too much transparency makes these kinds of rotations overly difficult to visualize (and poorly so).
P := A -> plots:-display(orientation=[-90,15,-160],
r=0..4, theta=0..A, coords=cylindrical, filled,
scaling=constrained, axes=normal, style=patch)),
plots[animate](P, [A], A=0..2*Pi, frames=17, paraminfo=false);
This may be similarly resource intensive as an animated use of 3D plots:-shadebetween (for a similar number of frames). I could probably improve it by ditching the filled option in the plot3d call (inside P), and using a grid=[...,2] cylinder instead. That's done pretty well before -- the cylinder shape can have varying height, to joint the two surfaces where they don't intersect within the desired domain. Let me know if memory/GUI performance is a huge issue.