It’s always DNS lol
“Quite within the realm of someone who’s got some computer skills” means “inaccessible to most people”. I don’t mean to sound like an ass about it, but most people just don’t care enough about this stuff to invest even a bit of time in it (nevermind the upfront cost for a Synology or Qnap NAS).
Realistically, the best solution is hosted and managed versions of FOSS apps where the private data is encrypted. Most people just don’t want to manage a server, and this solution would provide funding to FOSS projects while also increasing data sovereignty for non-self hosters.
As much as we all might want it to, self hosting will never be mainstream.
Why not exclude the folder you want to move from the initial sync, and sync that folder separately to the final location?
Think about how many people have a Synology NAS; it’s close to what you’re describing, but it’s still a relatively niche product. People simply don’t care enough. What you’re describing could definitely work, but only once people start caring about this.