I had considered hacking the executable file (taskmgr.exe) to see if there were a way to build this into it, but went with a decidedly easier and less risky method.
Since it amounts to a standard list-view control, what I did was to write an application that can detect if Task Manager is running, and if so, to hook into its list-control and perform the sort (by simulating a column click; I didn’t feel like manually sorting). It took a while to get it to be flexible enough to account for variations (especially since the columns are customizable), and then to allow for sorting on a different column—I figured I may as well have the option.
Unfortunately it means an extra program running in the background, but I already have plans for incorporating it into a more general-purpose app so that it’s not a one-function process, thus making it more acceptable to have it running because it does more things.