...is there a way to sort the results of the saved search in a way that doesn't affect the other saved searches?
No. Each view (Main, Context, Folder, Search etc) will remember one set of show and sort settings. This feature is often requested and it is "on the list".
You really don't need a custom search to get this info quickly. Here is how I do it: I always keep the Due Date view on All Tasks, showing everything except completed, subtasks inline, and sorted by Due Date. (when sorting by Due Date, I find no need to switch to the Overdue, Today, Tomorrow tabs, since you can see all of this info in All Tasks.) To find timers I go to the Due Date view, and click on the Timer column header. Voila, all your timers sort to the top. To resort the view, I click on the Due Date header. Done.