A colleague just pointed me at this issue. What's the problem exactly? I see in the code that the manifest has:
It also needs the READ_* permission likely. That should give it full access to external storage. Storage Access Framework is a completely different system for interacting with user documents across apps, has nothing specifically to do with write access to sdcard.
And you've always needed that permission to read/write sdcard without root. Old apps didn't have it. The change in KK is that you can now read/write to your private data folder on sdcard WITHOUT needing the permission -- you only need it if you want to touch outside your private data.
So is the real problem that syncthing doesn't USE external storage (sounds confusing, but it only has the WRITE permission), doesn't expose it to the user as a target, or is there simply a bug under the hood somewhere...
Hope that helps!