When UPNP is enabled in your router and PS4 is put in to DMZ [DMZ is key!] NAT type should always be Open [unless your ISP has restrictions in place or uses CGNAT]. As you said, sometimes you need to back out the game and go back in for it to refresh.
Have had some PS Chat Party issues in the past when PS4 was not in DMZ, where party chucks you out and states there's a NAT problem...
Your NAT type will most likely be moderate/strict if -
1. you do not have the PS4 in DMZ.
2. Your upload and download bandwidth is too low
3. Your MTU is set too low [set it to 1500 ADSL and 1492 for PPOE... Automatic usually works fine]
3. Wireless connection [possibly] rather than wired.
4. 3G/4G/Sat/MiFi connection [Cr*p for gaming]
5. Piggy backing neighbours' connection! [nobody does that tho!!]