The Thunderbolt is a large handgun capable of shooting a burst of three bullets in such close succession that it is almost as if they come out of the barrel at the same time.

Burst first simulated via a standard AEmitter rather than Azukki's rather neat bullet spraying wound alternative. I would like to get the bullets to spawn closer together to get them to match with the above description, but when I make the ParticlesPerMinute much more than it is I was getting the same gab between the first and second bullet, but then often having a fourth or fifth bullet near the second and third bullet. I tried to go with three AEmitters with different StartTimeMS and StopTimeMS times, but either could not get it to work at all, or caused a similar problem to the issue I was having with a ParticlesPerMinute much over the 4160 that it is now.

Ejected casings could do with some work getting them to fly through the air less uniformly. They are currently three casings attached to a null.bmp object that I was hoping would have a weak enough joint that they would fall off. Previously I had been trying unsuccessfully to get them to be an object that gibs into three casings instantly on spawning, but I could not get that to work either.

I also suspect there is something off about the offsets, since it destroys itself rarely on shooting.

In a .lua file attached to an invisible object that gibs the three casings:

FireIgnoresThis = 1 or something like that should fix that problem.
Or move the muzzle a few pixels forward.

No, he's using emitters so that won't work.
You should switch to TDExplosives so that the rounds inherit the velocity, that way you won't hit yourself no matter how fast you're moving assuming proper muzzleoffsets.

I probably do not have a proper muzzleoffset. I essentially just copied the offsets used by the Ronin Desert Eagle, but later tried to follow the offset tutorial on the wiki, but that messed things up so I had to revert it.