Shortly after posting my question I came across AutoRaise. It supports warping the mouse to the center of a window selected with the application switcher and giving the window focus after a user-definable delay.
(I actually forgot that I had stumbled across AutoRaise last year on an old MacBook. I got the pings of memory after posting the question and then dusted the old MB off and found it. I'm not sure why it never came up after exhausting what I thought was every way of searching for this behavior.)