Have you considered storage autoscaling feature. Transaction logs are critical for recovery.
I'd suggest you to check Managing capacity automatically with Amazon RDS storage autoscaling and see if this helps in your case.
Here is a related re:Post thread.
Hope you find this useful.
Comment here if you have additional questions, happy to help.
Here use s3 bucket to store logs and then monitor it, you can use lambda function to store logs into s3 bucket
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