How to extend Nighthawk X10 R9000 via wired ethernet with same SSID?

[Jedermann]

I appreciate any advice on this problem.

I have an apartment with two walls between my Nighthawk X10 R9000 and the main room. The signal is too weak to be useful. After trying two Ethernet over the AC systems without much success (~20mbps) I've now paid to have Cat6 connecting the back room where the Cable-to-Ethernet box and my Nighthawk X10 R9000 are to the main room.

I would like to purchase an Access Point for the main room that will use the same SSID as the backroom so my IOS devices can roam back and forth. In the past when I have tried to use the same SSID every device would still connect to the worst signal. For example, I would try to use my laptop in the main room and it would automatically connect to the backrooms Access Point even though the main room Access Point was much faster and closer.

What Netgear device can I buy that will work with my Nighthawk X10 R9000 router allowing me to use the same SSID?

Configuration would be:
CableCompany->CableComponyBox->ethernet->R9000->ethernet/Cat6->[TBD Device]->WiFi->Client devices

Is the "RAX20 AX1800" the right device? Another?

Thank you very much!

[plemans]

For it to be as seamless as you'd like, you'd need to upgrade to a mesh system like orbi or mk nighthawk. 

The when the other devices are hardwired in, they don't function as a mesh. You can use the same ssid as you've found out, but devices tend to be sticky and not roam. The Orbi/mk nighthawk support the smart roaming protocols while using a wired backhaul.