OK,well,in truth,I have never even held a Sigma,and so I am not a Sigma tech.IMO,this guy is not the mentor to choose to teach you how to work on yours.Some clues,using a jewelers screwdriver for a drift punch to knock out pins.We use a drift punch.The claw hammer to hit the screwdriver.Its a PR thing,if you are gouing to make a gunsmith video...
Then ,grabbing the pin to pull it out with the needlenose,the serrations in the pliers jaws are likely to bugger up any pin softer than the pliers.Then there is the re-springing with a ballpoint pen spring,I tried something like that on an FN FAL once.Not recomendable.There are outfits like Wolfe who sell spring kits through Brownells/Midway.
His wife's manicure emery board.I have used those on plastic and such,but NO for what he is doing.We do not hold a part in one hand and an emery board in the other and wave our hands back and forth.No.We use a vise.Holding a part in your hand rounds everything.You have no control.
His motion was stroking side to side,in the same direction as the lines,No.We stroke perpendicular to the lines,We are cutting the high spots off the lines as we cross them,and we watch the low spots uniformly disappear(I understudied a Master mold and die polish man)
Did you notice his shiny spots on the edges and his darker unpolished center? He is rounding everything out.His Polished" surfaces are now lower,and ineffective.Ony the part he did not touch,in the center,now works.
I would use a Gesswein mold polishing stone,maybe 600 grit,maybe 900,an EDM or some medium hardness that would break down a bit to conform.I would grind a little shape on the stone to get started,and stroke the length of the profile of the part,across the grind or wire EDM lines you see,and in the directiion of function of the mating part,I would watch the low spots of the tool finish and keep my progres uniform.And,I would not take all the tool finish off.As soon as I thought the mating part would smoothly bridge the low spots,Id stop,They hold lube and trap grit.
You may try another post asking"Who is a good,reliable smith to do an action job on a Sigma?" and see what you find out.
FWIW,I consider myself an amateur,hobby smith. I don't take in work,I have no FFL.