I feel stupid after figuring this one out, but it's obscure enough that it's worth posting the answer in case someone else has the problem.
At some point in the past, while attempting to fix another DNS issue, I had modified the registry key for the DNS service to include a PublishAddresses parameter that included the address in question. Once I modified this value to remove the old ip address, everything worked as expected.
More details on this issue can be found here:
Quotes from link:
You shouldn't have had to alter the reg to make this work. From the
reg entries you showed, it indicated that the DNS service was the
culprit registering this data, and not the Netlogon service. DNS will
register itself due to the NS records must reflect the correct FQDN
and IP address. I would suggest to check DNS zone properties for the
NS records. Make sure they are showing the new IP address. Once that's
correct, I recommend changing the reg entries back to default, which I
don't believe the ListenAddress and PublishAddress STR or DWORD values
are in there by default. You can export that key before deleting them,
then go back and run an ipconfig /registerdns and restart the netlogon
service. Check to see if the correct IP shows up.