The ideal solution is to end up with one, and only one, filtered outlet which you connect your modem to, and run extensions from.
Your current master is in the wrong place, but by keeping your existing NTE5 and adding a NTE5C you will end up with two master sockets, and that should be avoided.
The only easy way to do what you want legally will involve two filters - one filtered faceplate on the NTE5 and another, likely of the dangly kind, where the modem is sited.
I would do it so:
1. Purchase a filtered faceplate for your NTE5, making sure it has both "AB" and "235"(might be "2345") connections on it.
2. Run a secondary socket from "AB" on the filtered faceplate to where you want your modem.
3. Run another secondary socket from "235" (yes, use "3") on the filtered faceplate to where you want your extension phone.
4. At the modem socket use a decent dangly filter (if BT supplied one with your modem it should be a decent one) to connect your modem and other extension phone.
All of the above wiring should be at least CW1308 (twisted pair) standard. The CW1724 you mentioned is fine.
Note that this does not use your NTE5C at all to avoid the double master situation.
Other members may suggest other routes to doing this.