I've been working on this ever since the server move. I have found various things wrong - I.... don't have a list of what on what day, alas.
Most recently, I opened a ticket with cPanel because it seemed that the old IP was appearing in various places, but it appears as of today that was only true in old log files.
They also mentioned the slow lookup and suggested that it might clear up in 48 hours propagation, which........ doesn't really make sense, but I'm weak on DNS skills. grr.
I'm opening a ticket with NameCheap to see if they can see anything on their end.
edit: Nope, but I didn't realize there were dns zones for ns1.pc2.io and nc2.pc2.io. 'A' records in there were wrong; corrected now. D'oh!