For cast bullet use in rifles I recommend the gas checked ones like the WFNGC and it's brothers (Veral Smith's LBT designs).
Beartooth Bullets, Cast Performance, Oregon Trail (LaserCast - TrueShot), and Leadheads have all sold me good quality cast bullets that I shoot from Mach 1 to above Mach 2 in 44mag, 44supermag, and 444marlin.
Montana Bullet Works also make high quality LBT and other style bullets.
I would get them sized .431 or even .432 as .44 rifles, especially microgrooved ones, have somewhat larger bores.
Be careful if your rifle has a 1/38" twist as it will cease stabilizing heavier, longer bullets somewhere as you move up the line depending on the velocity.
I would stick with bullets 280 grains and lighter in the 44 magnum in a 1/38" twist.
1/20" twist you can shoot anything your shoulder and general constitution can handle.
My favorite cast bullet for the mag and supermag is the CastPerf. 260gr. WFNGC.
18-19 grains of 2400 in the case of the 44 magnum.
It should do well out of your Henry at 1500-1600 fps or so.
I go to the big 300gr. WFNGC in the 444 Marlin.