I used IMR 3031 for years in heavy hunting loads in my '86 45-70. Also have used IMR 4895 and Hodgdon's Varget. 

Reloader 7 has been working very accurately in full loads for my 38-55 and 45-70s-both in the neighborhood of 1750fps
Have not tried it yet in my 40s. But that would be a prime choice to try.
I did find an accurate load for my 40-72- 25 gr of 4759 
when I was fire forming brass.
Please note that the Lyman Cast Bullet Handbook no 4
lists smokeless loads for the 40-70 Sharps Straight. That is
very close to the case capacity of your 40-82Win and the data should be a good starting point.
Powders listed such as 5744,4198, 3031, Re 7 and Varget
with bullets up to 420 gr
One thing, your bullet molds are probably all plain based.
You need to protect the base of the bullets with something
for all but light smokeless loads. I use 0.060 LDPE wads
under 210 gr Pl Base bullets for a load of 15 gr Unique for fire forming my 40-65 brass for my rebuilt orig Hi Wall.
BUT, with the 40-82's short neck, you cannot take a chance for a wad to drop off inside the case and away from the bullet base. 
Hope this all isn't confusing, and helps you along the way.
Interesting to me to report your results as I have another '86
pending a rebore or a 40 cal replacement barrel. Have considered a 40-65(40-2.1) with its long neck, and still allows for a bullet nose out further from the neck.
The 40-82 is a 40-2.4" and so to feed from the mag of the '86, you cannot have a long nose on the bullets.
Of course, you can load singly with longer nosed bullets
but they may not clear the chamber if you have to unload a chambered loaded round. May have to "slip" the extractor.
beltfed/arnie 

Arnie, I just learned more about loading for mine than I have in all the time its been mine. 
It don't show up very often, that data for it. 

Don't have any experience with the 40-82 in that heavy a projectile but here are some results from an RCBS 40-260 cast bullet sized to .406 in an antique 1886 original barrel:

IMR 4198  28.0 grains  1428 fps

H 4198     28.0           1510

IMR 4759  23.0           1425

AA 5744   27.2           1610

Nope shoots a 16 twist, 80 grains of Swiss.

For those not familiar with the 40-82 "silhouette", it is the 45-90 case sized down to 40cal. Remains a straight-tapered case rather than the bottle-neck of the original 40-82. Steve Rhoades' reamer allows for sizing down 45-90 cases with no or minimal trimming. IIRC, there are two other similar cases. One is the Crossno 40-82 and the other is one from Shiloh. Don't know the specifics of these.