Cron job on shared hosting account using some random IP on the shared server?

I recently was forced to migrate to a new shared hosting server by my hosting provider because of issues they were having (mostly related to hacking and spam blocking) with their old server. So now I'm on this new server and have a new dedicated IP for one of the cPanel accounts I have on this server (which has a few add-on domains, but it's mostly used for the main domain associated with that cPanel account). I have a piece of web software on the server that takes emails from an account on the server and processes them into the web software. This requires a cron job to be run to check/download the emails. The web software has a security mechanism built in so that it will only allow the cron job to run under authorized IP's (that I can set via the web software configuration). On the old server, the IP that the cron job ran under was the main shared hosting IP (even though I had a dedicated IP) - that was fine though since I knew it wouldn't change and I could therefore set it in the web software security settings and it would work. However, this new server seems to be running cron jobs under some random IP assigned to the server - it is not the main shared IP, nor the dedicated IP for that cPanel account, nor any other dedicated IP I have for any of my other cPanel accounts. I'd like it to work either the same way it did on the old server (where the cron job used the main shared IP), or for it to use the dedicated IP assigned to the cPanel account. Having it just use some random IP on the server worries me not only because I don't control that IP, but because what if it changes and my web software stops running, or something else - there are just too many variables for me to consider that safe. The problem is the support team for my hosting account has not had any luck getting this accomplished thus far and seems to be clueless about how to get it done. Any thoughts/suggestions/help? Thanks!