The odds of the current chamber matching the dimensions of a .30-40 reamer with the only difference being the neck are slim. You're opening a can of corned beef hash which could either be tasty or garbage. Best case it'll go according to Hoyle, worst case it'll require setting back so as to perfectly clean up the chamber, but that opens another can of poor fit of fore arm and repositioning of the fore arm anchor to the barrel.

My thought: do a chamber cast of the current chamber and compare it in detail to the reamer. Perhaps a new barrel is in order, and retain the old barrel for posterity or for switching back and forth.

I also had a 6mm Krag also known as a 6mm Womack.

Cases were difficult to make and never lasted long before the shoulders would crack.
Plus .30-40 Krag or .30 US Army cases are getting more difficult to find.

I set mine back and made it into a 6mm Remington.
Shoots better than a .243 since my barrel had a tight twist to shoot heavier bullets.

Yes it can be rebored to the original .30-40 Krag or rebored to a .38-50 Remington Hepburn or a .40-60 Maynard which use blown out .30-40 Krag cases or the slightly shorter .303 British cases..

What an odd looking case, I experienced cracks at the case head, headspaceing on the shoulder cured that problem.
Mike

I am dumb but happy, why can't you rebore to 30 caliber with whatever twist you want and then have the gunsmith run in a throater to open up the chamber to 30 caliber?  Not being an old gunsmith I have no idea what problems might occur.  I am presently having JES rebore a rifle of mine and he was really good about answering my questions.  I had to leave a message as they work with noisy machinery and he called back the next day when he had a quiet moment.  The price to rebore, rechamber and mail back was less than the cost of a barrel blank.  Look for my recent post in this category on "Who rebores to 50 caliber" and you will get a list of quality businesses who can answer your questions.  I used (You need to Login or Register to view media files and links)
I am not sure your primary use for this rifle but I hunt deer and antelope with a 6mm-30/30 Improved and a 25-35WCF single shot and have taken some large mule deer.  I also have a 30-40 Hiwall and a 30-40 AI Borchardt and my am about to go on my first black bear hunt with the Borchardt.  I don't think you could go wrong with either the 6mm Krag or a 30-40.  Tom

He does list prices. $250 for 3 groove, call for 4 or 5 groove. 

I paid $350 for a rebore, rechamber, fit the extractor, cut two dovetails and return shipping.  It has been about two weeks so maybe I will get it soon.     In the meantime I have gathered up everything I need to reload for a 50-70.  Tom

Did JES take over Cliff LaBounty or was it Delta does anyone happen know.