If you go with the slowest powder choices you'll get the biggest boost from the rifle, but a lot of flash and blast from the pistol that won't produce better speeds than with medium powders like Blue Dot and 800X.
I have to disagree with part of this. It has been my experience that the slowest powders, (2400, 296, H110) produce more speed at max loads, in both pistols and rifles. Yes, you do get a lot of blast and flash from pistols, but I get higher velocities with those powders than I do with Blue Dot. (I don't use 800X so I can't say about that one).
A point to consider when you are looking for "one load to run them all" is what do you want that load to do? Proper bullet selection is vital for game use, particularly in the .357.
The common and popular 125gr JHP is designed for optimal performance at handgun speeds. Add another 500fps that the carbine can deliver and the bullet can be seriously overdriven, resulting in a radical change in impact performance. The Marlin carbine can push a 125gr to 2200fps and at that speed, they tend to expand so much and so fast they seem to blow up. Penetration suffers a lot when this happens. The 158gr JHP/JSP tend to do better, their heavier weight, means somewhat lower speed from the carbines and their construction is generally such that they don't usually turn into the "grenades" that the 125s often are.
Contact the bullet makers of the slugs you are thinking of using and get the velocity range the bullets are made to perform in. There are slugs that will do alright at 1800fps but not at 2200fps.
If you're not shooting game, it doesn't matter much, but if you are, its something to know and account for.