I'll concur with checking on your smith's preferences.
If you are going to key in on cast bullets,some have deeper rifling.Brown comes to mind.
I just got a Kart in.It looks good.The bore finish is real shiny.Rifling looks fairly shallow.
A comment was made about how well the tube itself will shoot.Could be that brand vs brand,we'd have to be pretty good shots to take advantage of the accuracy advantage.
I'm no expert,but I would guess Scheumann has worked pretty hard on the accuracy development.
Here is where you will gain most of your accuracy.The sights are on the slide,and the barrel moves within the slide.
Generally speaking,any drop in barrel will have some extra clearance someplace.That clearance means the barrel has options as far as where it is pointed.It will shoot bigger groups.
One place you can help is at the bushing.No perceptible movement,but free to tilt 1 degree to unlock.No bind on the barrel.
Given the variability of slides,rails,etc..everything will have some extra steel to fit,now.The hood will be oversize.Many drop in commercial hoods are pretty sloppy.Thats windage variation,and slop in the headspace and locking.
So after the hood is fitted,a little bluing/hardfitting assures the locking lugs engage properly,the firing pin centered,and the "Up" travel of the barrel stops in the proper lug engagement.
That is half of controlling vertical dispersion.
The next part is cutting the barrel underlug,so the feet rest on the slide stop with the barrel at full lockup.Most folks cut that with a special tool,blind inside the frame/slide assembled.Then the underlug has to be radiused to match the correct length link.That done,the breech end of the barrel has no vertical play at lockup.On the underlug of the barrel,the two feet straddling the link,provide two resting spots on the slide stop pin.A 12 oclock contact on top of the locking lugs is a third point of contact.Breech is located
And,once all that is done,the sights and the barrel point in the same direction,same way,every time.
There is more,timing(verifying the bbl/slide sufficiently unlock for clearance) and link length and the radius on the underlug.
Use blue,assemble,try,file a little,re-assemble.
Then,when all seems right,Check it all again with the dynamics of firing.
Good chance its time to tune an extractor.
I'm trying to say what you are mostly buying in a new barrel is some extra steel in all the right places.
That will only help if you have someone with skill and tools to fit the parts better than a production drop in barrel.
Not everyone does.The ones who do ...you might figure you will have to pay.
Its meticulous,time consuming work.Time is money.
I'm an amateur hobbyist,not a smith.
I bought that Kart barrel to replace a (new) Clark barrel .The only thing that was wrong with the Clark barrel ....I was learning about all that stuff I just wrote!!I had tunnel vision on one problem as I created another.
I'm calling it "Tuition and experience"
Most of $200 for a new barrel and I still have to do the job!!So it may have been cheaper to pay a good smith.
But that would be too easy.