I took advantage of the Apple Support chat to discuss this issue. After three multi-hour sessions over two evenings (and a rabbit hole to chase when one of Apple Support's steps caused my computer to revert to 10.10 Yosemite Server), the conclusion is that all hope is lost.
High Sierra (10.13) is the most recent software my hardware will support, and High Sierra will reportedly not see an iTunes that will recognize iOS 13.1.2 or later devices. There's no going backward for the iOS devices, either. This means no device backups (I do them locally, not to the cloud) and no iTunes updates. Interestingly, Photos still sync but I won't be surprised when that breaks too.
My only resort is to dig a iPhone 6s out of my dustbin and enlist it to host my traveling tunes, and not allow iOS to update. Ever.
I guess there's an outside chance Apple will apply a fix to iOS 13 but their track record's not so good. tvOS for tv 4 doesn't regularly send play count or time updates back to the Mac when using AirPlay, And nothing syncs via WiFi to iTunes any longer even before the 13.1.2 debacle. My old iPod Classic still syncs! Lol!