Re: 44/357 mag Accurate #7 or #9?
I can't speak for the .44mag since I don't load for it. A friend of mine does use AA#9 in the .41Mag though to push 210gr jacketed bullets for a deer load.
AA#9 was my favorite slow-burner for heavy .357mag loads. I never loaded it behind 125gr bullets though, just 158, 170, & 180gr.
I've never used #7.
Not much info but hope it helps. Maybe others are using stuff closer to your chosen combo.