I presume you used B-Tree indexing in PostgreSQL vs hash-indexing in BDB & your own code? PostgreSQL does support hash-indexing, but the documentation suggests it's not faster than B-trees anyway (probably because it would involve a second disk access).
Let's be honest though - this is an incredibly niche use-case. There's nothing in the relational model that precludes supporting this use case optimally, but in practice engineering resources get focused on more mainstream uses. You did your due-diligence and found that support for your scenario was lacking in existing RDBMS systems. That's great, but I think you should be qualifying your support for NoSQL lest others with traditional use cases (best served by RDBMS systems) simply copy your conclusions where they don't apply.
Let's be honest though - this is an incredibly niche use-case. There's nothing in the relational model that precludes supporting this use case optimally, but in practice engineering resources get focused on more mainstream uses. You did your due-diligence and found that support for your scenario was lacking in existing RDBMS systems. That's great, but I think you should be qualifying your support for NoSQL lest others with traditional use cases (best served by RDBMS systems) simply copy your conclusions where they don't apply.