Software for adding supports to 3D printed miniatures in STL file
I don't think you'll find automated software to create supports "the way I want them to look."  So...

It might be worth investigating the "Advanced Properties" of Cura to see how thin, and thinly spaced, you can set its support walls to be.  I know there are settings for reducing the thickness at the top of the support, as well as some sort of "top gap" setting, for just the kind of problem you're dealing with.