That's really, really strange. I sit behind an IPv4 NATting router whose policy is "default REJECT unless the packet is related to a connection that conntrack knows about". [0] The device also runs UPnP, but Signal never attempts to forward any ports. Full disclosure: I have good IPv6 service, but textsecure-service-ca.whispersystems.org doesn't have any AAAA records, so I don't see what that would have to do with anything.
My friends and I can use both Signal text and voice messaging without issue.
Just what sort of obscenely restrictive firewall are you behind?
[0] You know, a typical NAT firewall configuration.