If I took the job on, would begin with a press and a wide plate to cover the top end and support between 2 places, this could easily done with 2x4's, once fairly straight, look for bulges or dents, I do not have a dent raiser, but those things are cool, after removing any dents, would get back on the press and proceed, a mandrel could only be used once you got the barrel fairly straight for the mandrel to enter and I don't think would be necessary, previously mentioned, gentle bending of barrels to get point of aim works, just make sure the stock fits you 1st. Stock fit has more to with poa, than barrels usually. Just a guess, but I the reason real target shotguns, meaning competition, has to with taking the shotgun, and I am talking mostly about over and unders, and the smith, taking the gun to the range, patterning it, and seeing how the regulation between the 2 barrels are, and then taking it back as many times as it takes and tweaking until both barrels hit poa, and very fine choke fitting. I do mean fine guns like Perazzi.
I have made a dent raiser using and allen wrench and a round steel rod, as long as it is within 6" of the muzzle the octagonal shape of the hex key, will push the steel rod into the dent, but you are limited to how long the hex key is.