To ensure that none of the application instances have external IP addresses while still being able to access Google services like BigQuery and Cloud Storage, two effective methods are:

1. Enable Private Google Access on all the subnets (Option A): This allows instances without external IP addresses to access Google APIs and services through Google's private network, thus avoiding the need for public internet access.

2. Create a Cloud NAT, and route the application traffic via NAT gateway (Option E): This method provides outbound internet access for instances without external IP addresses by routing traffic through a NAT gateway, which allows the instances to access services like BigQuery and Cloud Storage without exposing them to the public internet.

Options B and C are not correct because Private Google Access is configured at the subnet level, not the VPC level, and Private Services Access is for connecting to managed services, not for accessing Google APIs. Option D is incorrect because BigQuery does not support VPC peering.