Folks, all may not be lost here!
I actually called Apple Support yesterday, and worked my way up to their chain to an iOS 9 product specialist. When I explained my situation, he fully agreed that this was a serious issue, and that he would talk to the developers on both the iOS 9 and iTunes sides, although he said he couldn't guarantee me anything.
He called me back about 6pm last night, and said that the iTunes team had released a 12.1.3 version of iTunes that was both iOS 9 and Vista compatible, and that he would be emailing me the download links. When I got the email, and followed the links, it took me to a page to download iTunes, but the text on the page said it was for version 12.1.2, posted April 2015. Since that would be older than the 12.1.27 version I already have installed, I emailed the support rep back, asking if this was truly the right links, or if the text on the page just hadn't been updated, as I didn't want to accidentally make things worse by installing a back-leveled version.
After I sent him that email last night, it occurred to me that if they really HAD created a new version of iTunes to fix this, that maybe it would be automatically found by the Apple Software Updater now. So I started Apple Software Updater, and sure enough, it now found iTunes version 12.1.3 as available! I let it download and install, and viola! iTunes would again sync correctly with my Vista desktop!
I don't want to provide the links here that the support rep gave, since I'm still not sure he sent me the right links....but I'd suggest that everyone having this issue do what I did, and go run the Apple Software Updater, to see if it also finds a new iTunes version 12.1.3 to install on your Vista (or maybe even XP!) machines!