There is no reason why it would not work. You probably needed play around w/ the primer, powder granulation, & lead/tin alloy to get where you want to go.
As one psoter stated, you'll need a BP- lube to keep the fouling soft.
You may already know this, but when done shooting decap & wash the BP residue out of the brass cases. Otherwise, the residue will weaken the brass & cause it to fail.
Many shooters dump the brass into a jar of soapy water @ the range. When home, de-cap & then was the cases w/ a brush & warm soapy water followed by 2 hot water rinses. You need to decap & wash the cases as there is no way of removing the BP fouling from the primer pocket w/o removing the primer.
Seat the bullet & the over-the-powder-wad so they do not protrude beyond the bottleneck. Otherwise, the wad will act as an obstruction & gas blow by can/will melt some of the bullet & cause leading.
Will this be a single shot or a bolt gun? Sounds like this migth be an interesting project.
The 44-77 the 44-90 aren’t even close. Per “Handloader’s Guide to Cartridge Conversion“:
The 416 Rigby case -- 2.90” long -- case capacity 132.56 grains of water.
The .44-77 Sharps & Rem -- 2.25” long -- 87.52 grains of water.
The 44-90 BN -- 2.44” long -- 92.71 grains of water.
The 44-90 Rem St --2.60” long -- 92.13 grains of water.
The 44-90 Sharps BN --2.63” long -- 102.57 grains of water.