My Consideration:
The request flow for Roadrunner APP considering the design of architecture is NGINX - AWS ELB - EC2(In fact the Roadrunner).
I suppose that the NGINX works as proxy which just logs the request and the APP which is large-scale.
The Web Server (NGINX) needs to a Logrotate system for sure and
I suppose that The Tasmanian Devil doesn’t need to read logs from Roadrunner in real-time to generate reports, I will work in this point.

The first point is setting logrotate system up which designed to ease administration of systems that generate large numbers of log files.
It allows automatic rotation, compression, removal, and sending log files.
Defining policy about the file /var/log/nginx/access.log with appropriate size file, compression and structure name(i.e setting data suffix up in the end of the name) and then sending the file log to AWS S3 using AWS CLI.
The amount of data transferred will be optimized and it won’t send replicated log file.

With the log file at AWS S3, We can use AWS IAM to create an user with specific permission which Tasmanian Devil will be able to read the logs and process (could be insert in a database to make easy to generate report).