You may be right about the Quattro side, but how would enigma2 automatically know about that side? Unless like you say, the switch is 22KHz automatically on that side.

I think this switch could be viewed in enigma2 as TWO multi-switches tied together.
Ports A thru H would be Switch One.
Ports I thru P would be Switch Two.

(Two Ports assigned for each satellite, 1 for vertical, 1 for horizontal)

If this line of thinking is correct, then try:
Assign switch One the proper diseqc switch number (1-4 or A-D), and also use ToneBurst A
Assign switch Two the proper diseqc switch number (1-4 or A-D), and also use ToneBurst B

Is it possible to test this configuration on a satellite or two?