For those who don't watch the videos I have recreated some of Brian's work regarding Slave 1, asteroids and kilotons . I'll post a link to the site with detail analysis later. If I can figure out how to to upload and paste pictures I'll post the analysis here too for ease of reference.
Preemptively I understand that many asteroids (some way smaller than the one I'm even talking about) were not vaporized or even melted, merely fragmented or split apart. This shows a disparity in firepower and not a contradiction, because the asteroid i refer is most explicitly superheated melted and probably vaporized, it was very large.. and very near the end of the chase...
This sorta does imply the shots we see at the beginning are a thousand times less powerful than the shots near the end (lol), and RoF didn't change so it ain't easy to explain...
I'm just looking at what the gun can do, at maximum power (and its impressive!)