Just spoke to Square-Enix about this. Here's a copy of my chat log with the agent:

System 11:34：You are now connected to SEE Agent Tony.

SEE Agent Tony 11:34：Hi there, I am sorry to hear that you are having connection issues.

SEE Agent Tony 11:34：What server do you play on/

SEE Agent Tony 11:34：?

Customer 11:35：Hello. My character is on Excalibur (NA).

SEE Agent Tony 11:36：Are you playing on PC?

Customer 11:36：No, I'm on PS4. My ticket number is [REDACTED] - that describes the issue I'm having.

SEE Agent Tony 11:37：Okay, I will email you some troubleshooting steps to try in a moment. Once you have tried the steps please reply to my email to let us know if they helped.

SEE Agent Tony 11:38：Other than this issue, is there anything else I can help with?

Customer 11:38：No, you don't understand - this is not a problem at my end. This is happening with dozens of other people as well. Have you not seen the Technical Support forums?

SEE Agent Tony 11:39：I have seen them yes.

SEE Agent Tony 11:39：The issue has been reported

SEE Agent Tony 11:39：It may be related to a denial of service attack on North American data centres.

Customer 11:39：Can you ask someone at your end to respond, please? Everyone feels like they're being ignored.

SEE Agent Tony 11:39：I do not have direct contact with forum moderators.

SEE Agent Tony 11:39：We are the account and technical support team.

Customer 11:40：Alright, but what good do you expect any generic troubleshooting steps to have?

Customer 11:40：You are aware that the issue isn't at my end.

SEE Agent Tony 11:40：The steps I am going to send you help with a range of network issues.

SEE Agent Tony 11:41：If you do not want to try them that is okay.

SEE Agent Tony 11:41：Would you like me to send you the steps?

Customer 11:41：Sure, send them if you genuinely think they have any chance of helping.

SEE Agent Tony 11:42：Other than this connection issue, is there anything else I can help with in the mean time?

Customer 11:43：No, since I can't play the game. If these steps don't work, I'll be in touch again, whereupon I hope my issue will be treated as more than a generic connection problem.

SEE Agent Tony 11:44：I will be in touch as soon as I can, allow about 20 minutes for my email. Thank you for visiting the Square Enix Europe Support chat line. Take care and have a good day!

As you can see, they're aware of the issue, but have no resolution yet. They really have no idea what's causing it. It might be due to the DDoS attacks. My guess is that they're blanket banning / restricting connections from certain IP address ranges they suspect to be linked to the attack, which is having a knock-on effect on innocent users. I suppose it's only to be expected - a handful of us not being able to play, or a much larger mass of players experiencing lag and complaining? It's pretty obvious that we're acceptable collateral damage and don't matter.

I'll try the steps they suggest. I'll post them (and my results) here. But don't expect an official response to this issue until the Forums team wake up from their 4th of July hangovers.