I have one and there is something you need to know if you are planning to shoot fixed ammo. The case is too small at the mouth to hold a groove diameter .410 bullet. The best I could do with mine  was .405" diameter I tried turning down necks and what I got when I loaded a lead bullet was a jacked bullet coming out of the muzzle and a case that was suddenly 1/2 inch shorter. These rifles were made for paper patched bullets which are bore diameter.(.403 or so) and black powder. If you intend to shoot fixed I recommend black powder FFG and a paper patched bullet. These can be loaded by seating bullets into the case with your thumb. No seater required. All you need is a way to remove and seat primers. Anyway that was my experience. (They are really fun to shoot that way.)

I don't know if you have any machinist experience but I made my own sizing die for .40-70 SS by starting with a .30-40 Krag FL die annealing it and cutting it down on the lathe. I cut the die off at the shoulder so that the case would come out fairly straight. at least the area that stuck out the top of the die. a little measuring allowed me to cut it at the right place. If you had some reamers you could also leave the die full length and drill and ream the neck area. Just an idea.

If you can get past the heresy of doing so with an original rifle, you could have a 'modern' reamer run into the chamber to open it up a bit.

In my old 40-70 Sharps I used a Lyman 410610 GC bullet with just the GC portion inserted in the case like a heel bullet and it worked fine for 200 yd shooting, at 215 gr its to lite for long range shooting. I used a un lubed bullet and a IMP-CO grease wad behind the bullet and it worked well, as you didn't get any grit in the lube groove.  The groove size in my bbl is .412. .

I had already tried the 41 mag die and still won't chamber. If I run them in my 38-40 die a little I can get a case in but it ain't pretty so I was looking for other options.

A friend of mine had one of these and it had the paper patch chamber. It would not take a groove diameter bullet unless the case wall was turned to .003 - about the thickness of heavy foil. 

He got the guy that ran the tool grinder to grind back the shank of a 3/8" boring bar to permit boring to about 2.75" deep. Then he leaned on me to bore his barrel out.  I set the barrel up in a 4 jaw and bored the chamber to give .004 clearance using expanded RWS 9.3X74 brass. This was about 20 years ago before Hornady .405 was available.  
After dialing in the chamber I looked through the bore with the lathe turning at low RPM. The bore flopped around like a jump rope. The hole must have been crooked about .040 but the old rifle shot well one put back together. 

The proper dies can be determined by using the size of the smallest bullet you might use.
Add the thinnest case wall you might use times 2.
Say you will use a .408 bullet
the case wall is .011 X2 = .022
.408 + .022 = .430 = the loaded round diameter
Then subtract .002 or .003 depending on your preferred case mount under size 
for me it is .002
.430 - .002 = .428 inside diameter for the die or smaller.
Most .40-65 dies measure .421 with Redding being .418.
I think the most economical .40 Sharps Straight dies  are those made by Lyman. Lyman might tell you what they measure. I know that RCBS will tell you what their dies are made to.

"The ASSRA was founded in 1948 as an orginization that promotes the responsable use, study and preservation of single shot rifles".  Arn't there enough tables at gun shows filled with butchered and otherwise altered original single-shots?  If you don't care to learn how to prepare the ammunition these rifles were originally designed for..why not re-barrel to a more re-load friendly caliber...and save the originality (and barrel)  for future collectors?