Awesome post! I think that you and I have done very much the same process trying to figure this stuff out. These pictures are fantastic and very similar to the ones I looked at under the microscope we have in the lab, but wasn’t sure how to take a picture of with a cell phone. I think one interesting thing is that the laser affects the glass in all different directions, and that the scoring tool has some noise on the surface, but is essentially producing deep cracks in the direction of the tool travel. This is consistent with the shards produced by breaking the glass - with the scoring tool, which broke the glass easily where I scored it, there were few shards but they tended to be long, thin and skinny. Like terrible splinter fodder. 
With the laser, I could break it occasionally along the ‘score’ that I wanted, but often could not, and further more, all the breaks produced many small crumbs of glass, that were small and roundish. (potentially the glass that was inside the scallops of the laser path from your pictures?) I believe that the low success on breaking with a laser score has to do with the stress from bending the glass doesn’t know where to travel, and therefore often seems to veer off in random directions. With a scoring tool, which is producing long clean cracks in the glass, the stress from bending runs along those lines more readily and will travel around some pretty interesting paths.
I also had some problems with the high heat causing cracks. Someone suggested to use a wet paper towel over the glass for better engraving, which I haven’t had a chance to try as an aid for cutting yet. (However, on top of all the things you did, I also tried soaking in some cutting oil, which I’m told seeps into the cracks and helps ‘push’ the glass apart - did not help)
??