could you describe what you're after more precisely? The way Zotero's own bibtex functionality works, it doesn't have stable citekeys. They're generated on the fly on export by nature of the data model (since they're not stored, you can't generate them at any other time). Better BibTeX does generate them on import, so you probably want to use that.

works for me with standard BBT settings. Contact the developer through his github page, but make sure to read his notes on reporting bugs/problems so you get him all necessary information.