If it's normal residential service, the ISP will typically only provide one dynamic public IP address. If the ISP's router is doing NAT, I would contact the ISP and have them turn that off. Then create a VLAN and VLAN interface on the 1234P facing the ISP. Configure one switchport in this VLAN as a DHCP client facing the ISP. This will receive a public IP from the ISP.
Set up your private network on the default VLAN (or create a new non-default one) and NAT from this VLAN interface to the public VLAN interface. Now your 1234P is acting as a DHCP client to the ISP and a server to your LAN. DHCP from the ISP won't cross between the VLANs. Either use IP domain-proxy or manually enter the ISP's nameservers (or public ones) in your local DHCP pool.
You can leave the ISP's NAT in place but I wouldn't recommend it as double-NAT often doesn't play well with some applications (SIP as an example).