"So the question is, can I detect whether I am singletasking or multitasking in a taskwindow? I know about <Wimp$State> but that seems to say 'desktop' in both cases, so that doesn't seem to be a solution."

Answer: You can detect this using the SWI TaskWindow_TaskInfo,0.
It returns in reg r0 a zero when it's not in a taskwindow.