Lee Precision make a set of .577 Snider dies, which are probably the most economical .... so anyone who carries Lee Precision products can probably order a set in for you - not likely something most dealers would keep on hand, of course ....
These dies tend to size down the neck of the case too much for most needs .... I believe they were designed to emulate the case-mouth dimensions of original .577 cartridges (which always used an under-bore-size expanding bullet) ..... and also so cartridges loaded with them would fit in the tightest possible surviving chambers .....
Most surviving Sniders
don't need the case sized down so much ..... if at all. ..... Full-length sizing with the de-priming/sizing die from this set accordingly ends up causing excessive working of the brass, because the case mouth just gets blown out to near full chamber size each time it is fired .... then gets necked way down again on reloading, and so on.
You could certainly use the sizing die in initial forming of your cases from 24 gauge brass shotgun hulls .... but, as mentioned above, if you are going to be firing the cases in the same rifle each time, you would be best to subsequently use that die for de-priming only.
Another important reason for wanting to avoid sizing down the case mouths so much is that the overwelming consensus of opinion among Snider shooters nowadays is that much better and more consistent accuracy is achieved by using an
over-bore-size bullet (ranging from, say, .485" up to as much as .600") rather than the sub-bore-size bullets originally used (and for which these dies seem to be designed.) By the way, some people report getting good results, particularly with the slow-twist (1 turn in 78") three-band Long Rifles, just using a .590" to .600" round ball pressed into the case mouth, instead of an elongated bullet.
Keep in mind that when the original Snider cartridge was developed, they were just emerging from the muzzle-loading era, and didn't seem to have a grasp of the concept of a larger-than-bore-size bullet for best engagement of the rifling, which of course became standard for breechloaders. Instead, they kept trying to use sub-bore-size bullets with expanding bases, as were used in the muzzle-loading Rifle Muskets .... and never did get them to work properly.
The base skirt of a Minie-type bullet must be able to expand at the very instant of ignition of the powder charge ..... but a similar bullet loaded into a cartridge case is constricted from doing so until the base of the bullet clears the case mouth! Even though the Snider-Enfield system was a temporary 'stop-gap" pending adoption of the Martini-Henry rifle, the British War Department went through no less than
nine versions of the .577 cartridge between August 1866 and August 1871, trying to achieve consistent results! (It apparently never occurred to them to try a larger-diameter bullet .....

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