Whoo guns. So how's this going to end? The Japanese way when guns were introduced, or the American way with the natives trading for weapons and sometimes being on par in battle? Though in the end I'm sure their world is going to look like Africa once all the major battles are done.
As for not going from blunderbuss->modern. Happens in real life as well just look at Africa. Went from spears against Roarke's Drift to AK-47's against Rhodesia. All in less than 100 years and no muzzle loading in between. Only major weapon development there, was to have kids use them in human wave tactics. A Beretta design as shown in the manga might be a bit more difficult to replicate but something like an AK-47 would be insanely easier as the hardest part would be the rotating bolt. A Martini-Henry falling block would be easiest but it's only single shot.
As for rifling it's not a dark magic only the most secretive engineers can conjure up, just run a rotating rod that scrapes the inside of the barrel bit by bit, people do it all the time in their garage. Hardest part is the correct rate of twist but that's why you test before mass production.
Though all that said this is a world of magic so I'm sure enough wind/earth/fire magic and they'll skip past Khyber Pass quality weapons in no time. They want a REAL nightmare weapon to introduce? artillery. Just have a row of howitzers pull up a mile away and shell the hell out of your target like you're reenacting WW1 or Alnus hill in Gate
https://www.youtube.com/watch?v=426XL910eKI.