With that 1/19 ROT I would suggest a bullet from a Brooks mould that has the profile like the originals usEd in the past. I spent a lot of time shooting the .44-77 and the .44-90 BN both with the 19 ROT and I have not found a bullet that shoots as well as the original profile at ranges as far as my sights elevate.
I just pulled a bullet from a case to measure the dimensions that works so well in my .44's
I use a .485 gr 1/20 to 1/30 alloy .430" diameter 1.325" long. For the .44-2-5/8 (.44-90 bn I use a .520 gr because with the extra velocity it has it handles the longer 1.425" bullet in fine shape. The Brooks mould is adjustable. I opted on a .430" diameter so I had the ability to patch thin for shooting without fouling control when hunting and still patch to a snug bore fit.
The .44-77 is a great caliber and the bullet I use has dropped three Buffalo in fine shape. Two with the 77 BN and one with the 90 BN.