Loading data to ES cost comparison

A customer is currently crawling the web and writing to S3 + loading to Amazon Elasticsearch. The current architecture looks like this.

ECS -> EC2 -> S3 -> EC2 -> ES

Looks like they set this up a long time ago, and would like to optimize the workflow. They are using ECS (they have containerized old code written in C#), running that through EC2 to write to S3, and then using another EC2 instance to load data into ES. This seems like a very inefficient solution. There also seems to be a lot of unknown around ECS and crawler code, and they would not like to touch it. Given this information, I thought the following architecture would make more sense.

ECS + Kinesis agent -> Kinesis Firehose + Lambda -> ES (and S3 through backup)

What I would like to know is

1. Does the above workflow make sense?
2. Customer is concerned about price. While it is difficult to get an exact estimate, I was hoping to get some insight into if anyone has done a similar comparison. This customer has a small team and would not like to commit resources to end up with a more expensive solution.