Obligatory reminder that Mongo is shit and you should never use it for data you care about.

Reliability-wise, it sucks. Maybe it's gotten better recently, but I still probably wouldn't trust it.

But is there a document store out there that's faster than MongoDB?

There are quite a few better options for trustworthy databases. One is my employer, MarkLogic, which is an ACID compliant NoSQL document db with a lot more indexing capabilities.

Especially if you’re using the search tools to retrieve data, I think a properly indexed MarkLogic would be quite a bit faster, and still more reliable.

https://github.com/pingcap/tidb https://github.com/cockroachdb/cockroach

They provide the features of both RDBMS, such as ACID transactions, SQL, and the scalability of NoSQL.