It is impossible between those routers. W8970 has only WDS mode.

Very important - service/server must act on these ports when you make a test (something must listen). I think that you understand me.

You have to disable DHCP server on the second and third router. Connection without port WAN.

How do you check it?

I think that W8816 will be good solution for bridge mode in your network.

Poor line causes that modem inside your TP-linka reduces the speed of the internet to gain a more stable link (lack CRC). Maybe your old device has better ADSL modem. In my experience I know that...