Schuetzen rifles tend to be single-purpose rifles.  I have a Uberti High Wall in 30-40, and a Martini-Enfield in .303 British and I have messed about with an Olympic-type Martini in .30-06.  All 3 will shoot plain based lead alloy bullets accurately enough to be used as Schuetzen rifles. But the Uberti is a reproduction of a 19th Century hunting rifle and the M-E is a military rifle.  Schuetzens they ain't. The .30-06 Martini is set up for offhand shooting and has all the Schuetzen bells & whistles, but it is just too darned heavy.

If you persevere, cases are not all that hard to come by, even if you are just starting out. 50 or 60 should last for a long time.  I prefer (above all) the 28-30 Stevens and then the 32-40.  For me, the 8.15x46R runs a distant 3rd.  I have not had enough luck with the .25s to look upon them with much glee.  Some of it is tradition, more important to some people than to others.  Some of it is perceived recoil.   

All we are doing is punching holes in paper at 200 yards or 40 rods, but with as much accuracy and uniformity as we can muster.  Bullet velocities are in the 1400 fps range, maybe a bit faster and maybe a bit slower.  It does not take much of a powder charge to achieve that.  What is important is shot-to-shot uniformity.  Smaller cases, and especially (to me) straight-walled cases position the small powder charges more uniformly than do the larger cases, and the small powder charges also occupy relatively more of the volume of the smaller cases.  Look at the "modern" cases used with "modern" single shots for Schuetzen competition.  The 32 Miller and the 30-20 are examples.  Both have relatively limited powder capacity.

If you have a single shot chambered for 30-40 Krag and are considering Schuetzen, perhaps you might get some cartridge cases from RMC that are solid brass & have only a bore-sized powder space.  Those, along with breech-seating should make a 30-40 very competitive.

the internal ballistic dynamics of "straight walled" (or very slightly tapered cases are different from those of bottle necked cases.  while bottle necked cases are capable of excellent accuracy the american schuetzen technique involving breach seating simply seems to work better especially in the leisurely paced match routine we enjoy.

If you are talking about offhand shooting, with and/or "fixed" ammunition, different strategies can come into play, and fixed ammo-30-40 rounds might fare well.  I can also recommend the use of custom cases that use a thick-walled internally straight walled powder chamber.  they will reduce capacity and makes shooting them in our ASSRA-schuetzen manner a lot easier---and possibly more accurate to boot.  I have had such cases made for a non-standard (approximately) 11mm BN Mauser stalking rifle and also 220 Swift cases to turn them into a sort of extra-long 22 hornet for cast bullet use.    the custom made cases were no more expensive that trying to find some of the other oddball no-longer produced cases.

   As euro-schuetzen sport evolved into International Free-Rifle Competition, rifles that were basically identical to Schuetzen rifles continued to be used, but strengthened and improved to handle 20th century military match ammo-----bottle necked high velocity jacketed-bullet stuff  (I have a swiss martini of that type and era in the modern 7.5x55 military ammo)  They can shoot very well with cast bullet loads (as can 30-06 Springfields) but they will never most-likely be winning bench rest rifles.

The 30/40 can be made to shoot competitively. I have one in a HW with a 12 twist, A&M heavy barrel.

The standard case can give good accuracy, I think with 14.0 gr 4227, I could get 3/4" groups at 100.

I machined 2 cases for it, one with a 1/4" hole back to the primer pocket (1.9cc capacity) with .312 in the neck area to be able to seal the chamber and the other with a straight .312 hole back to the primer (2.8cc).

Both where successful and loading BSed but, I got my single smallest group from the 2.8cc case and that's just a little smaller than the 30/30. Pictured is the 2.8cc best group. As I remember the group size is .318.

Frank

In looking at Uberti's web site, I only see their 1885 offered in various .45 caliber cartridges. Will a beginner have to hunt down a used rifle to get started if he chose a .30-40 caliber? The only place I see with new stock is Buffalo Arms. Or is BA the only source of this caliber?

This is my 3040 Krag.  Target not great.
Kurt