Howdy,
I like the hyphenated cartridges, too. .44 WCF bullets are quite common! I use Meister, Lasercast, Magnus, and my own cast bullets. Most commercial bullet casters use Magma moulds, so whosever bullets you buy, they will be the same 200-grain, bevel-base RNFP as the next guy's.
Slug your bore! Groove diameter for the .44-40 should be .427", but I've seen them as large as .431". Rule of thumb says to use a bullet that is .001" larger than groove diameter. I shoot a modern Marlin 1894, EMF Hartford revolvers, and an Uberti 1873. I try to use .428" bullets, but will settle for .429". .430" will sometimes refuse to chamber and .427" isn't quite tight enough, but will still shoot good.
I use Winchester brass because it is very thin, hence more internal space for black powder! I load on a Dillon 550 and use Hornady one-shot case lube spray on the brass. I like 6.5 grains of Unique, but the new Trailboss powder is quite impressive in large capacity black powder cases. My new favorite load, that I would hunt with, uses Hodgdon's 777 and a 200-grain bullet.
Basically this is not a .44 magnum, and although your rifle is quite strong, this cartridge case isn't the one to hold all that pressure. The thin brass really seals the chamber well, so if you choose to shoot black powder, 99% of the soot will be trapped in the barrel. The greatest thing about this bottle-necked case is the tendency to fall into the chamber easily, and pop right out when empty.
Enjoy the rifle. You will, of course, have to buy another in .38-40.
Bitterroot