Theoretically, you should be able to take the ethernet cable from the Actiontec and connect a new router to it (whatever brand you choose) and let that router handle all of the business. You will also want to disable the wireless broadcast capabilities in your Actiontec router, so as not to add to static noise on your new router's broadcast channel.
Also: Before you try buying a new router, try disabling WMM in your Actiontec (not sure why, but some people have had bad luck with this default 'enabled' option):
1. Login to your router (192.168.1.1).
2. Click on 'Wireless Settings' at the top (2nd item from the left).
3. On the left side of the screen, click 'Advanced Security Settings'.
4. Scroll to the bottom of that new page and click on 'Other Advanced Wirless Options'.
5. Click 'Yes' on the warning screen.
6. Scroll down on that new screen and click on 'WMM Settings'.
7. Uncheck the box next to 'Wireless QoS (WMM)'.
8. Click apply and let the router save the settings (takes up to 30 seconds).
WMM gives multimedia precedence over all other network items. In the case of your security system, that result can be conflicting with the priority levels of the surveillance system. The conflict may also cause your security system to believe that the stream has failed when it has not.
Good luck! Note that if you are not sure of how to accomplish the goal of having 2 routers together, just get ahold of a FiOS technician and tell them immediately what you want. Most of the base-line techs will need to transfer you to a system tech.