Be sure to put the "T" on the higher port of the water block. Right now I have my only "T" in the exact location as you fill tube "T".
As millions have informed me from this forum,

I have my "T" in the wrong place! (I already knew that but Sh*^ happens).
So I was thinking of just leaving the existing "T" and adding another as you illustrated in you sketch.
The image below shows my setup, radiator is out back connected with copper. My second "T" should be installed on the high (left) block barb.
Jim