Just use a splitter to split the coax that goes to the dvr. Now it may or may not work but you have to try. Also if it works you may or may not have signal issues.
Since your ActionTec provides WiFi, having iton the 2cnd floor is better as it should be at a high point within the home. However if you don't use WiFi then m oving the Router will be a moot point. It would be a matter of moving RG6 cable (with good F-Connector ends) to the new location.
In your present location, the Router is most likely be connected to a splitter. Follow the cable in the 2cnd floor location back and down to that splitter and remove the cable from that splitter. Then you will have only two connections on tghe splitter. One on the Input and one on one of the two output connectors. Remove the splitter and replace it with a back-to-back female F-Connector (availble at Radio Shack and places like Home Depot). If the Router will be placed near the TV Set Top Box, you will need to have a length of RG6 (with good F-Connector ends) and the splitter you removed. Where the cable went into your TV Set Top Box, you would connect it to the Input of the splitter. On one of the two output connections, it will be connected to the TV Set Top Box. The other goes to the ActionTec Router.
If you are not ready to use a F-Connector compression tool and make your own RG6 cables or this sounds complicated to you, then call Verizon and have them relocate the Router for you (Verizon will charge you for the service).
Also one thing to consider is the new Quantum speeds of 150/60 and above are connected with a CAT5e or CAT6 Ethernet cable to the routers WAN, if you ever plan on an upgrade. They would probably run the new Ethernet cable and switch your router. If you plan to stay at somewhere like 50/20 or 75/35. Your probably in good shape. Providing you have a good RG6 cable and clean connections.