Returning to the subject of disjoint 2CT's, I have been searching your b134679 pattern (12 x 2CT) with various configurations of 12 disjoint 2CT's in b258, thus giving a total of 24 x 2CT's.
So far I have found only case where reduction testing allowed 4 x 2CT's to be removed, and so my best result is currently 20 x 2CT .