It slipped my mind that I had posted about this here. Here's an update!
I did contact support, and got a reply a couple hours later. I was told that:
Your server has been experiencing high loads recently. This is causing
all services to lag. The loads are being created by poorly written
scripts that users are running that hog CPU time. We are actively working
with these users to reduce their CPU consumption and everything will be
back to normal soon. I am very sorry for any inconvenience this may have
The support person, Patrick, offered to move my domains to a "more stable server. " I went ahead with that, and approximately 24 to 36 hours later, I was notified that my account had been moved. That was on the evening of 7/6. Since then, I've had no problems. So thank you, again, Patrick!