Using an Application Load Balancer in conjunction with EC2 Auto Scaling across multiple Availability Zones is the most resilient option for maintaining service continuity and client session state. The ALB offers session stickiness, which is crucial for stateful applications to maintain user session information across requests, hence its suitability for an eCommerce workload. Auto Scaling ensures that upon an EC2 instance failure, a new instance is provisioned automatically to replace the failed one, preserving the desired capacity and performance levels. Directly deploying the application on S3 with Amazon CloudFront for static resources does not cater to the stateful nature of the application. While RDS Multi-AZ does serve as a resilient database solution, it does not facilitate high availability for the application layer itself. Utilizing Elastic IP addresses does not inherently provide failover for instance failures and lacks the capability to automatically reroute traffic to healthy instances.