That doesn't get you out of having to face the problem. This is not a challenge unique to MongoDB or other NoSQL databases. Oracle or Postgres might be ideal for your transactional data store, and a columnar database might be ideal for your analytics.
I suppose you could choose one of those options and sacrifice either your customer experience or your analytics, but it's probably better to use the best database for each use case.
But I don't want to be just snarky. We faced the very same dilemma and solved it in a similar way - we use Apache Spark, which can connect to MongoDB directly. It loads fairly quickly and we can save it to Parquet on S3 directly, the whole thing is about 5 lines of code.
If you have a Spark platform in place, it's a decent solution for this.
A more complete answer is to dump your data into a columnar format into S3 and then use one of plethora analytics tools that can work with this format (AWS Athena and Drill are mentioned, other tools like Presto, Spark, Redshift Spectrum or BigQuery can help).
