I don't understand how double NAT would cause a problem: you send a UDP packet out to someone on the public Internet (maybe STUN) and it will punch two holes; a

I don't understand how double NAT would cause a problem: you send a UDP packet out to someone on the public Internet (maybe STUN) and it will punch two holes; assuming you don't have low quality symmetric NAT, packets sent to the outer NAT on the egress port will be translated to the egress port on the inner NAT which will translate back to the original port on the client. Why do you think this would fail?