I tried to do it only on the longer front part, and it doesn't work. Unless I don't understand correctly what you mean by "interrupt the automatic extension of the fillet along tangents by avoiding the very small radiuses"
I tried only for the front (green) lines and most of the part desapear (was cutted) after I did the fillet. I also tried only the front top line, which is not near a curve and it did the same thing.