What should a solutions architect do to resolve this issue?

Explanations:

Disabling source/destination checks allows the EC2 instances to forward traffic that is not destined for their own IP address. This is necessary for the proxy servers to properly route the traffic from the private subnets to the internet and back. By default, EC2 instances are configured to check if they are the intended destination for the traffic, which would block the forwarding needed for proxy functionality.

While adding a rule to allow all traffic between instances with the same security group may help with communication between EC2 instances, it does not address the primary issue of forwarding traffic to and from the internet. The traffic must still be able to exit the VPC and return appropriately, which this option does not ensure.

Changing the DHCP options set to point to the proxy EC2 instances for DNS resolution is irrelevant to the issue of traffic forwarding. DNS settings will not affect the routing of traffic to the internet; they only affect how hostnames are resolved to IP addresses. Therefore, this option does not resolve the forwarding issue.

While adding an additional elastic network interface could theoretically create a path for traffic to route properly, it complicates the network configuration unnecessarily and does not directly solve the problem of traffic forwarding. The EC2 instances still need to have source/destination checks disabled to act as proxies effectively. Simply adding a second network interface does not address the core issue.