I think the pipe you are asking about was fitted by vw years ago on a vehicle recall. The reason for it was that the heater matrix was prone to failing and hot water entered the footwell. There is a fix by fitting a mk3 matrix which is a direct replacement. Alternately just remove it and either fill the gap with a piece of pipe or replace the pipes altogether. On rereading it i note you have replaced the matrix so i would just remove the valve and either bodge the joint or replace the heater pipes.
can you confirm its not the membrane? Try opening the door and poor water onto the outside of the window and check if the seal is keeping the water out.
The nearside front is a very short line just runs to a joint on the bulkhead offside is also quite short. This is from memory from when I replaced mine. I bought premade prebent pipes rather than making the pipes myself.
