Mark said
"What do I need to do to change the IP address of the Elite doorbell, or otherwise work around this issue?"
Hi Mark,
You can use ConfigTool to find the doorbell camera on your network and edit the IP address.
I have attached some images to assist with the process.
Modifiying IP using ConfigTool
Download and extract ConfigTool, locate the configtool.exe application in the folder, and run it.
In the ConfigTool interface, click on Search Setting and enter the username/password of the Doorbell camera in the fields.
Find the DB camera in the list and edit the IP address to a static IP address of your choosing.