You are incorrect. I can not speak for halal, but in Kosher slaughter minimizing pain IS a primary goal.
You have completely skipped the stringent rules about the knife in your summary, so perhaps you are just not aware of it.
The knife must be razor sharp - the slightest knick renders it unusable. The knife must be drawn in a single motion, any hesitation, or pressure, while cutting makes the animal not kosher. The location of the cut is precisely defined.
All of the above are there to minimize pain, because the knife is so sharp the animal doesn't feel the pain, any pressure on the wound would also trigger pain.
> or only on the first and last one (kosher)
This isn't correct. Only one blessing is said, and not saying the blessing does not render the animal not-kosher. The blessing is about the shochet, not the animal. This is different in Halal were the blessing is the primary thing that makes the animal halal.
> whether slaughter can be performed by any believer (halal) or only by a specific priest (kosher, only Sachets (a type of rabbi) can perform kosher slaughter)
The shochet is not a priest. Being a shochet is 100% about knowing what to do, and 0% about any kind of special status. Anyone can be a shochet, including women. And you do not need to be a Rabbi, you just need to be trained.
> bolt pistol
A captive bolt pistol has an unacceptable high failure rate. You can NOT consider them more humane than Kosher slaughter.
On the religious details of the status of the shochet and the number and character of formulations uttered by him (or, apparently, her) I can well be wrong, not being an insider and as such only having access to the (often only partly correct) information which is available to outsiders - although there is also the possibility of there being several 'truths' for different rites or sects. This is also mostly besides the point in this context.
On the minimising of pain I'm not wrong. Captive bolt pistols and electric shocks can be misapplied and that certainly happens in some cases. In the majority of cases these devices fulfil their purpose in that they knock out the animal before the knife is applied. This knocking out is instantaneous, contrast that to the slow death by oxygen deprivation which is what happens in halal and kosher slaughter. A sharp knife only makes the cut itself less painful, it does nothing for the minute-long death process which follows.
> although there is also the possibility of there being several 'truths' for different rites or sects
There is not.
> On the minimising of pain I'm not wrong
You are. You are simply misinformed on the topic, yet writing with authority you do not posses.
> for the minute-long death process which follows.
There is no minute-long death process. Insensibility happens within 10 seconds according to Temple Grandin. Additionally when done properly the animal appears not to feel it. (https://www.grandin.com/ritual/rec.ritual.slaughter.html)
I also know this personally because I visited a shechita plant and watched them. The animal collapsed often the moment the shochet removed his knife. To me the worst part of the process was the cattle prods used to move the animal in line (the cattle really hated that). The actual killing was very painless.
Captive bolt stunning is LESS humane then Shechita. Every piece of evidence shows this, but people think "if it's new it must be better".
The only benefit is in cost - Shechita is very expensive because of the necessary training. Captive bolts need little training. But they are not better for the animals.
You have completely skipped the stringent rules about the knife in your summary, so perhaps you are just not aware of it.
The knife must be razor sharp - the slightest knick renders it unusable. The knife must be drawn in a single motion, any hesitation, or pressure, while cutting makes the animal not kosher. The location of the cut is precisely defined.
All of the above are there to minimize pain, because the knife is so sharp the animal doesn't feel the pain, any pressure on the wound would also trigger pain.
> or only on the first and last one (kosher)
This isn't correct. Only one blessing is said, and not saying the blessing does not render the animal not-kosher. The blessing is about the shochet, not the animal. This is different in Halal were the blessing is the primary thing that makes the animal halal.
> whether slaughter can be performed by any believer (halal) or only by a specific priest (kosher, only Sachets (a type of rabbi) can perform kosher slaughter)
The shochet is not a priest. Being a shochet is 100% about knowing what to do, and 0% about any kind of special status. Anyone can be a shochet, including women. And you do not need to be a Rabbi, you just need to be trained.
> bolt pistol
A captive bolt pistol has an unacceptable high failure rate. You can NOT consider them more humane than Kosher slaughter.