Your setup sounds quite good and what you are describing is what i would also do. The alternative would be to add the pbs a second time with the login of pve01 in the DR case.
It sounds like, you just want to send mails. If this is the case, you can setup/use PMG (Proxmox Mail Gateway) for that. You can use it as a smtp server.
It doesn't need to be publicly available for that usecase, just make sure to setup spf...