Modeling graph data in Postgres?

Hi SQL colleagues,

Background:
I've been working on a public data repository that models data following
the schema.org approach (essentially an RDFa type structure), which yields
graph structures. Up to now, we receive the graph data initially nto
Postgres as "json chunks" and then our system decomposes them and feeds
them into Neo4j using the Gremlin language for indexing as a graph (we
provide some structured search services like freetext on the json within
Postgres too). Users then query the graph using Gremlin.

My problem is that Neo4j's indexing services have some painful performance
characteristics for our use-case (it takes a long time to reindex,
stability isn't great, single element index is slow). We've tried Neptune's
Gremlin support, with similar (unhappy) results.

Question for the group:
Does anyone have experience or recommendations for modeling graph data in
Postgres in ways that would viable for production use?

Maybe there are graph extensions available, or clever ways to make graphs
work within the existing Postgres/SQL environment? Ideally we could run
queries in Gremlin, but if we had to convert to SQL or another language,
that would be fine too.

Thanks for any input or support,
Steve