Isnt the only output on the 5216 an HDMI? If so, I cant think of another way other than just a long HDMI cable. Why not use a balun? Unless someone else has ideas, I think a balun type solution may be your best option..
So if one were to only go with the doorbell unit itself and plan to use the Mobile App for notifications while being gone, can you have the existing manual doorbell chime still function while home?