After some emails back and forth to Tech Support and my submission of a requested problem report, I got the following reply:
I requested that Parallels please remove some claims from the Parallels Desktop 9 for Mac: Updates Summary page (http://kb.parallels.com/en/117225), namely the following two claims:
Parallels Desktop 9 for Mac (build 9.0.24251) supposedly 'Resolves an issue with Parallels Tools installation in Ubuntu 14.10 virtual machines', from which readers (such as me) might infer that Parallels Desktop 9 supports Ubuntu 14.10.
Parallels Desktop 9 for Mac (build 9.0.24237) supposedly 'Resolves an issue with Unity mode in Ubuntu 14.04 virtual machines', which makes it look like Parallels Desktop 9 also supports Ubuntu 14.04.
From my experience, I've had no trouble with Ubuntu 14.04LTS under Parallels Desktop 9, but then I don't push the OS very hard. Upgrading Parallels Tools when upgrading 14.04LTS is miserable, but it can be done.
So... I'm going to give up trying to get Ubuntu 14.10 to work in Parallels Desktop 9 for the Mac. In all honesty, I never really expected 14.10 to work with Parallels 9, based on how past versions of Parallels worked with updated versions of Ubuntu. I thought there was a pleasant surprise when I read the upgrade notice for build 9.0.24251, but it was not to be. No real loss (other than several hours of wasted time).