Here's another approach that would be even easier - set up a web server somewhere that you have access to the logs for. Have a scheduled task on each router that fetches a page such as
http://mywebserver/name_of_router.html, on an hourly basis
Then, you can grep the webserver logs for the router name, and the last line found is the most recent IP address for that router.
Easy Peasy Lemon Squeezy