De-embedding S-Parameters of a DUT from three-port baluns

[RFbeginner]

Hey everyone,

I am currently trying to de-embedd a DUT that has on both sides of it 180° Hybrid Baluns
I have the measured 2x2 S-parameters of the boards and I have the 3x3 S-parameters of the Hybrids. the constellation of the board is as follow :
   

Hybrid(single-ended Input,Coupled Output)--DUT--Hybrid(Coupled Input, Single-ended output)

I first tried to convert all the  S Parameters to 4x4 matrices(filled with 0) and de-embedd the boards using the T parameters but it obviously didn't work due to the singularity of the matrices and the i tried to reduce the hybrid matrices to single ended input differential output and due to the fact that the common mode is negligible leaving the differential mode and he the Matrices become 2x2 and I tried to De-embedd the boards as shown in the picture attached

But still the results are not satisfying at all, does anyone know if something is off in my try or does anyone have another advice on how to de-embedd the boards ?

Thanks a lot