The issue related to bad external rotation and bad internal rotation: a reason can be that the shoulder blades are hunched together due to reasons such as too much sitting/typing work
where the hunched shoulder blades (like too much sitting, too much benchpress) can impair the rotation movements and
where the right arm in the internal rotation could not touch as of 2014 T7 let alone T3. The pictures are from UW Medicine Orthopaedics and Sports Medicine.
By this material here, the arm overhead is close to
- "external rotation, flexion and abduction of the right humerus in the shoulder socket" (B in the picture here)
while the arm underneath is close
- "internal rotation, extension and abduction of the left humerus in the shoulder socket" (C in the picture here)
so the problem as of 2014 was likely in internal rotation, extension and abduction of the right humerus in the shoulder socket.
The collage picture below is of 2016 where the major rotational movements have been fixed. The summary below lists the techniques I used to improve the flexibility where the last one with rolling on the floor was the most effective, particularly with a soft ball for the shoulder cap and foam roller.
Summary about the techniques to improve the arm cross stretching behind the back
a test here (found after reading Kate's comment here) with scoring, slightly misleading: you can also rotate the arms in the humerus that is not measured by the test
JohnP's suggesstion about swimming streches here where the page 24 awesome (parcticularly the picture 2 with external rotation)
rolling on the floor, relaxing, putting arm behind the back and softly testing different directions is an effective and safe way to improve the shoulder blades flexibility and the rotational movements