Hi, ok so there should be no reason that the other LAN ports perform any different to the first one, they are on a L2 switch bridge, so if there is odd behaviour it will be a serious mis config or fault.
NAT2 from my understanding is normal public IP with classic NAT.
Hi, great, but I suspect as other have said, if you stayed with CG-NAT and NAT3 (as you call it) you would have not had any issues, other than in you mind. As for the router not recognising your other PS4, that sound most odd.
It is probably worth eliminating all possible other factors before blaming NAT3.
Have you managed to successfully connect your playstation via ethernet cable, or is the lag you reported in your original post over a Wifi connection?
Try another ethernet port on the router?
Another ethernet cable?
Hook up a laptop where the PS4 is - can it connect?
Take the PS4 to where your computer is - does it work there?
Oh and just to clarify the previous questions asking what were you connecting to would have been to ensure that you weren't trying to plug a second cable into a Fibre ONT. It should go ONT --> Router - and plug everything else into that router.
Presuming you have fibre internet (also not clear from your posts)?