AWS routing "lost" packets intended to a network behind VPN

What you're looking for is Source / destination check - EC2 instances perform source and destination checks by default. The instance must be the source or destination of all the traffic it sends and receives. That obviously isn't true for gateways like in your case. Hence you have to Stop the Source / destination check

First select your instance:

Source / destination check

Then Stop the check:

Stop the check

Hope that helps :)