Is there any way to speed up changes to A-Name records through WHM/CPanel? I just had to do an emergency change of machines, but need to point our web panel software to the new IP address. Unfortunately, it is still pointing to the old IP after I changed it.
No. Those records are cached at other DNS servers. They will remain in cache on those servers for a time equal to the TTL. All you can do is wait for the cache to expire so those DNS servers will pull a fresh record.
Check out joeqwerty's answer on this question for information from somebody smarter than I am: