You could try changing the default DNS on the ps4 to google ones. these are 126.96.36.199 and 188.8.131.52 I can't tell you how to do it on a ps4 as I have an xbox one, but its not that hard. This guide might help?
I actually havent gamed on the xbox since i moved to TT. I have gamed on the pc and had no issues. My suggestion about changing DNS server addresses is that the TT ones could be over loaded with the amount of extra traffic with the lockdown.
Also, is your ps4 wired or wireless?