Hi,
yeah those saved objects cannot be pushed directly to the Elasticsearch index as you are trying. They are meant to be imported via Kibana again, which will take care of modeling the appropriate ES document for that.
There is currently an experimental (yet undocumented) API, that allows you to import those saved objects again into Kibana. You can find information about this API in this pull request. This (or using the UI) are the only ways to import those saved objects again.
Cheers,
Tim