Let's look at the differences in the systems.
This is the right-side view of the Poincare sphere (which Scheiber used and named the quadraphonic use for matrix after himself).
View attachment 79553
Left ch is cyan, right ch is red, inphase (lateral stylus) is olive, antiphase is violet, clockwise (stylus) is black, anticlockwise is brown.
A matrix can be defined on the sphere by stating a locus of points on the sphere for a trip around the room, clockwise beginning at front.
A great circle matrix is one that follows a circle of the greatest diameter around the sphere.
Regular matrix (EV, QS, DQ Ddi) is a great circle matrix with the clockwise room loci: olive-red-violet-cyan-olive.
Denon BMX and UD4 baseband make a great circle matrix with loci: black-red-brown-cyan-black.
Matrix H is a great circle matrix with loci: tan-red-blue-cyan-tan.
SQ is not a great circle matrix. It has loci: olive-red-brown-violet-black-cyan-olive.
UHJ is not a great circle matrix. It has loci: green-near_red-purple-near_cyan-green.
Playing the H recording in QS or RM has a reduction in F to B separation. It also has all of the phasiness of playing the recording in stereo.
Playing the QS or RM recording in H has a reduction in F to B separation. It also has all of the phasiness of playing an H recording in stereo.
Playing the H recording in UHJ works fairly well, with reduced separations all around.
Playing the UHJ recording in H works fairly well, with reduced separations all around.
Playing the UHJ recording in QS or RM had good front, but vague back.
Playing a BMX or UD4 baseband recording in QS or RM has no front to back separation at all.
Playing a QS or RM recording in BMX or UD4 has no front to back separation at all.
Playing a BMX or UD4 baseband recording in SQ works if you move the LB speaker to F and the RB speaker to B. Reverse the phase of the LB speaker.
Playing a UHJ recording in SQ works if you connect both LB and RB speakers to the RB channel.