What you might be better off doing is to physically move the master BT socket to where the rack cabinet is. You can get the pukka BT cable and jelly connectors off eBay.
You can then buy a surface mount box and an adslnation faceplate from
https://www.adslnation.com/products/xte2005.php
This replaces the removable front plate of the BT master socket.
You can then plug your broadband modem into the broadband port and the telephone patch panel can be hard wired to the terminals behind the removable Adslnation faceplate. All phones will then work through one single filter
This is assuming you have power at the location of the patch panels.
I have all the equipment in one location so no boxes or filters all over the house and a lot tidier.