First thing you need to do is establish the exact groove diameter since guns chambered in .32-40 varied from 0.318"-0.321" which is why some original Remington, UMC and Peters ammunition was loaded with bullets having a diameter of only 0.317" The throat will also need to be measured since it was somewhat common for the throats to be undersize of the bore as in the throat being 0.318" and the groove diameter being 0.320" - granted 0.002" difference doesn't seem like much but it can make the world of difference between an accurate rifle and one that is not.
If your particular bore in on-spec with a 0.321" groove diameter and the throat is also 0.321" and your reloading dies are, if necessary, honed to match the gun's spec's, there is no reason why you cannot run 0.323" cast bullets. If you try running oversized jacketed bullets, you'll run the risk of blowing it up in your face because of the increased and erratic pressure.
It is not uncommon and in many cases it is advantagious to accuracy to run cast bullet that are 0.001"-0.003" larger than the groove diameter. Assuming you're going to be running this rifle on black powder, you'll be casting bullets from a rather soft alloy anyway so there is very little pressure issue with the slightly larger diameter bullets. If the reloading dies are not properly sized however, you will run the risk of damaging the bullet upon pushing it into a neck that's too tight. I have seen modern bore liners chambered in .32-40 with a 0.316" bore diameter and 0.323" groove diameter (same spec's as the 8x57JS)
I doubt you're going to gain much of anything, if anything, going to a pointed or semi-pointed bullet. Most .32-40's use a 1:14 twist and when combined with lower velocities, the capability to build bullet RPM's will limit the bullet length that can be stabilized. Quality FN & RN bullets are plenty accurate for 300yd shooting especially considering they've been used for over a century at ranges well beyond that in the larger bores. My advice is to go with the heaviest FN bullet you can get to shoot the best. Sometimes the more you over-engineer the problem, the larger the problem becomes and the less answers you'll find.
"Carry the battle to them. Don't let them bring it to you. Put them on the defensive and don't ever apologize for anything."
Harry S. Truman