a few weeks ago my PS4's online became wonky - it could access the store and the browser, but could not load the friends list, what's new took forever to load, Bloodborne and DSII always gave me that 'you are offline' message whatnot
DMZ didn't work, port forwarding didn't work, rebuilding the database, restoring licenses didn't work.
Then I stumbled upon that MTU fix everyone was trying back in Dec 2014 when PSN came back up from being ddosed
MTU to 1473 worked for me. There is actually a more scientific way of finding your sweet spot MTU, but I settled on that and everything is working perfectly now.
Don't think that just because you already tried setting it to anywhere in the 14xx range that you have exhausted your options - my console is working now 1473 but I've read that once I set it to, say 1474 my connection will be back to nowheresville.