Which solution will meet these requirements MOST cost-effectively?

Explanations:

While a dedicated EC2 NAT instance can be cheaper than a NAT gateway, it still incurs costs for the EC2 instance, and it does not eliminate the data transfer costs associated with S3 traffic. Additionally, it would require management overhead and might not provide the same level of reliability and scalability as a managed service.

A NAT instance in the private subnet would not work because EC2 instances in a private subnet cannot have public IP addresses to access the internet or AWS services like S3. This configuration is not feasible for routing traffic to S3.

A VPC gateway endpoint for S3 allows for direct, private connectivity to S3 without using the public internet, thereby eliminating data transfer costs associated with NAT gateways and reducing overall costs. This option is the most cost-effective and efficient solution.

Provisioning a second NAT gateway would still incur costs associated with the NAT gateway usage and does not solve the fundamental issue of data transfer costs, as all S3 traffic would still be routed through the NAT gateway rather than directly accessing S3.