A couple of extra points that seme to be important.
Firstly chromosomal rearrangement is proposed to be the mechanism to produce macroevolution. Mutations to Hox genes have been demonstrated to produce macromutations - but chromosmal rearrangement has not. So there is no real evidence for this hypothesis.
The use of chromosomal rearrangements adds to a known problem of "hopeful monsters" - where does the "monster" find a mate. To solve this it is proposed that all ancestral species reproduced asexually. Needless to say there is no real evidence for this.
The additional problem of "hopeful monsters" - that slow refinement works more reliable than large jumps in "phenotype space" is answered by proposing directed evolution. For which there is no real evidence.
On this basis alone the semi-meiotic hypothesis seesm to be a very unpromising piece of speculation, far inferior to the theory that it is supposed to replace.