I also shoot a Shiloh Sharps 40/70 straight, and with the NASA bullet, too.
FANTASTIC gun (and bullet). I've shot a Browning 40/65 since 1998, and it was also was an outstanding rifle and cartridge, and when I got the Sharps in early 2005, I said to myself if the Sharps shot anywhere near as well as that Browning, I would be happy. Now, after 2700 rounds, I think the 40/70 Sharps actually shoots a bit better than the Browning!
My Sharps has a slight quirk: the throat is fairly tight. The RCBS 400 gr bullet has to be seated way too deep in the cases in order to chamber. I can't use it, and I can't use my Paul Jones 40 cal Creedmoor for the same reason. When I explained my problem to Bernie at Old West Bullet Moulds, he sent me a few samples of the NASA bullet. It fit OK, as long as the nose section just above the front driving band was around .400" or smaller. He made me a mould that cast that way. Even so, I have to seat that bullet right to the very top of the top driving band. In my mould that bullet weighs 402 grains in 20:1.
The only thing I don't like about the NASA bullet is that if you pan lube it, you can't "pop" it out of the lube cake. If you try to do that, a lot of the lube won't stay in the lube groove. You have to use a kake-kutter, which is OK, but it's slower and messier. I don't use a lubri-sizer - and I shoot the bullet unsized.
I use Buffalo Arms 30/40 Krag cases. No complaints.
My powder choice is regular Goex Fg. I load 70 grains of it, and at an OAL of 3.40", compression will be .15". MV is 1200 fps, and it shoots great! I usually shoot a match of 60 rounds with no cleaning - just blow-tubing.
I used to shoot 70 grains of Swiss 3F. Compression is only .05" so I can compress the powder during the seating of the bullet (without using a compression die). MV is way up there, at 1380 fps, so I especially liked it for 1000 yd. matches. There is one problem with this load - in hot and dry weather, I think it is fouling the barrel. I know that in hot and dry weather, I get unexplained misses, especially beyond about 500 yd. I have gotten away from this load and am sticking with the Goex Fg for now.
I use a .060" LDPE over-powder wad, and Winchester WLR primers, but in limited tests with the BR-2, it gave me more consistent ballistics. I expect I may eventually switch to the BR-2.
I've also tested an over-primer wad, but found no improvement in ballistics.
Good luck!! Let us know how it shoots.