I believe a header should work. When you say ‘single location’, do you mean region or instance ID? The logs should show both and it may be the same region is hit (probably the closest one) but that gateway/load balancer is forwarding the request to a different (specified) vm/instance.
An alternative approach would be to use the DNS name. You can send the request to a specific VM using:
<alloc_id>.vm.<appname>.internal
… but that would only work internally, not from the outside world.