Linux – DMZ IP and Private network IP

This may be a bit strange and any variations will help. We have a SIP server that resides on our private network with an ip 172.19.x.x . We constantly have problems with out LD Trunks reaching out because when the register they show the public IP of the router. I would like to setup one of the NIC’s on the 172.19 and one on the DMZ. We have about 1500 devices making the NAT very hard to work thru if on the dmz only (affects phones) or Private only (affects LD trunks).