Another enthusiastic Zotero user here. Current library has 13,775 items and for a low yearly price one can have multi-device sync and support the project. I'm also syncing to a server I own, for complete data ownership (just in case).
My solution: auto-export to a folder then sync using your preferred method. Use the betterbibtex plugin to rename and move all necessary files. Fiddly to set up, but reliable once it's working.
