One way of characterising a chunk is by listing its childless-descendants; for BACFE, those would be E and F. But in this case F’s feerate alone is 11, while BACFE’s is 13.2; which gives you an easy clue that splitting that chunk into [BACE,F] would be an improvement.
I think you could extend this comparison to create a compatible total order just by saying “given two diagrams, d_1 and d_2, then if x_0 is the earliest point where d_1(x_0) \ne d_2(x_0), then d_1 > d_2 iff d_1(x_0) > d_2(x_0)” ?
I think “prefix-intersection merging” then guarantees to produce a linearisation L_3 such that L_3 \ge L_1 and L_3 \ge L_2 according to that total order. I don’t think it guarantees that L_3 will be comparable to L_1 or L_2 according to the original partial order, but I think you’d need a fairly complicated cluster for that to actually occur.