I can't believe it, 20 posts and nobody has mentioned H-110 yet.
H-110 and 296 are the same or at the least very nearly so. The biggest difference I've noted between them is that 296 appears to be more temperature sensitive, at least when shooting in the SoCal desert. If that difference is still valid or if they are indeed now manufactured as one and the same I dunno.
Your final load could well depend on the Ruger cylinder length and how deep you'll need to seat the bullet. There are a couple of advantages of your using 360 DW brass instead of 357 brass. Trimmed to just fit to the throats you'll gain a bit of powder capacity and hold the front driving band fully inside the throat. Second and more important for your goals the 360 brass has a strengthened web over standard 357 brass. 357 Max brass could of course also be used with more trimming needed but again a stronger case. I don't remember off hand the difference of powder capacity between the three cases but in the FA I used the same charges with no change in chrono readings.
Rick