I have a situation where Dorico (3.1 30 day eval version) is drawing a slur through the stem of a flat. When I get the slur shaped to my liking and avoiding the flat, there is a natural space for an accent between the first slurred note and the star of the slur. While Dorico allows me to move the accidental down, as soon as I position it, it moves it right back up again (in Engraver mode).
There is a setting in Engraving Options>Slurs to disallow slurs from intersecting flats & naturals, you don’t need to reshape those by hand. There is also a setting under Articulations to allow accents to go inside slurs, but that’s project-wide; I haven’t been able to find a way to just change one locally, sorry.
EDIT this is what Behind Bars has to say about it:
Articulation marks in the middle of a slur go inside the slur. Accents at the beginning and end of a slur usually go outside the slur, so that the slur can remain closer to the noteheads. > An exception is when they would otherwise be too far from a note to be immediately apparent.
In other words: your desire to be able to do this locally is quite justified.