Sync MongoDB Replica set with Remote Replica Set
You can follow your original strategy with a minor tweak: add Google Compute (GC) nodes into the current replica set and keep them in sync until ready to cut over. The only thing you need to change is to set those new GC nodes to have priority 0. They will be full members of the set, they just cannot be elected primary (or trigger elections).

Once you are ready to switch over to the Google nodes, you need only reset the priority to 1 (or whatever your normal values are), and then step down or remove the AWS nodes from the set. You can guarantee that a GC node is elected primary by giving them a higher priority than the AWS nodes before issuing the step down.