Can you say how this part is going to be made, machined, molded or 3D printed?
Here's another workflow that gets maybe a little closer to what you want. It still doesn't transition to a point in the corners but it does leave the corner points.
In this example IF Alibre could loft between sketch 6 and sketch 7 and use sketch 8 as a guide curve I think that would give the results you want. The same thing would need to be done in the opposite direction with selective use of guide curves. I have had some success in the past creating Lofts similar to this but this one kills Alibre on every attempt. (If I had a seat of SolidWorks this wouldn't be too difficult to make with some surfacing tools. Just sayin'.)
You know, @Oldbelt
usually has good results with Lofts, maybe he will show up with an example to put our efforts to shame.