Two organizations each use Shared VPCs with some overlapping subnets; applications requiring private connectivity are on non-overlapping subnets. Provide private connectivity with minimal re-engineering.

Deploying a Cloud VPN gateway in each Shared VPC and establishing VPN tunnels between them is the most suitable solution. Cloud VPN allows secure, private connectivity between VPC networks, even across different organizations, and supports overlapping IP ranges by using Network Address Translation (NAT) on the VPN gateways. This minimizes re-engineering as existing subnet configurations can remain. VPC Network Peering is not suitable because it does not support overlapping IP addresses, which is a stated condition. Migrating projects and relaunching instances is a significant re-engineering effort, which the question aims to avoid. SSH port forwarding is not a scalable or secure solution for application-level private connectivity between entire networks.