Bro, sorry, don't game, don't have a PS4 so no practical experience on this. Just to clarify:

#1 - If UPNP is off, you get NAT3 but no "router will not support ip packet fragmentation" status.
#2 - If UPNP is on, you get NAT2 (which is what you want) but occasionally you have "router will not support ip packet fragmentation" status

Is that right?

#1 - How keeping UPNP off and forwarding the whole bunch of required TCP and UDP ports to the PS4. Will that get you NAT2 on the PS4? And hopefully get rid of "router will not support ip packet fragmentation".

or

#2 - Stay on UPNP ( and NAT2 )and ignore the "router will not support ip packet fragmentation" status. Does this affect anything gameplay or anything on the PS4?

Having said all that, the IP fragmentation error should not have anything to do with UPNP. What's the MTU for PPPoE set on the router? It should be 1492. Maybe something on the router (firewall,QOS?) is dropping packets and the PS4 network test is interpreting that as "router will not support ip packet fragmentation".

Sorry can't help much.
Router lah not modem. Turn off DNS Relay in /Service/DHCP. But it shouldn't have any effect on ping test. But if it helps, let us know.