I have never shot a 44-40, so don't believe everything I say, but here are some information on the 44-40 rifle.
The good news is that the SAAMI throat has a gentle leade angle. The bad news is the leade starts at cartridge diameter instead of bullet diameter. In other words, an oversize funnel, aka a "toilet bowl" throat.
Some cartridges can usually be counted on to closely follow SAAMI specs but the 44-40 isn't one of them. Barrel dimensions may be unpredictable. If it were my gun, I would make a throat impression to confirm the SAAMI throat and also to determine the groove diameter.
Some of the old black powder cartridges like the 38-55 will not chamber groove diameter bullets, since the cartridge was originally designed to shoot soft, undersize bullets that would obturate when fired. I haven't heard any reports of this problem happening with the 44-40, but be aware of the possibility.
Assuming it is SAAMI, it should chamber almost any 44 caliber bullet with a 0.280" crimp-to-nose length. Here's one suggestion. I would make the as-cast diameter big enough to use in 44 magnums and then size it down as necessary for the 44-40.