Yes, I understood that. And that was why I have suggested to also do source nat so that the route metrics become irrelevant. My theory behind that is that for reply traffic from your Mail-Publishing service back to the Internet the router would choose the outgoing WAN interface not due to the metrics but instead would select the one, the NAT session for the source nat is bound to (and hence the one, the connection initiating request came in).
But as we can see now, either you didn't manage to establish those additional NAT sessions, or you did, but it didn't help, because my theory is wrong. Anyway I'm running out of ideas.