The issue ended up being our host, Linode. The servers are located in their Dallax, TX datacenter and this datacenter had issues today from Nov 22, 05:42 UTC through to Nov 22, 17:02 UTC (just under an hour ago). Everything now seems to be resolved, and performance is back to normal.
This is the second such issue in as many months, so we'll be keeping an eye on whether we need to consider moving to another datacenter but as the saying goes "better the devil you know". The Linode status page is at
https://status.linode.com/ and if you see that showing a live Dallas issue at the same time diyAudio is having issues, they are likely to be related.