Want to add a wired Access Point to existing system. What should I get??

Your issue needs to include the distance from one end of the house to the other and obstructions such as walls etc. Mesh systems can work but the distance involved may require more than one mesh device to supply a good signal at the farthest distance. Your idea of not wanting to switch from one AP to the other would be a nice order to fill however, the quality of that WiFi signal will not be as good as running CAT wire to the other side of the house and then using another R6700v3 set up in AP mode for that side of the house. Typically, the devices sense the strongest WiFi signal and will switch to that WiFi if the two AP's are set up with different "channel numbers". This process is not perfect, some devices take a while to make the switch from the weak WiFi to the stronger WiFi. What's best about another AP is that you also have 4 LAN ports you can use as well as WiFi which could be used for solid reliable connections. The R6700v3 is a modem/router/WiFi so is the current R6700v3 used set for AP mode? It must be if its working. P.S. there is newer firmware for that unit as of Sept.