So, after a month of trying various things, talking to at least two Parallels support folks (in addition to Juczi), having the trial period extended so that I have a change to verify if this feature works before buying, I finally gave up and bought PD9 anyway. I figured I could always return it in 30 days if they don't get their act together.
Guess what: that fixed it. The feature is apparently not available in trial mode.
NONE of the Parallels folk, including Juczi, were aware of this. I always mentioned trial (same thing is said at the top of this thread) and I wasted hours trying various things, because support had me go through all sorts of stupid shotgun debugging like reinstalling and what not, instead of simply saying that it is disabled in the trial. At some point, they even lied that it doesn't work with 8.1 to get rid of me. Such level of incompetence is just appalling.