Here’s one way out - these pillowy shapes sometimes, often, even, lend themselves to a ‘loose loft’ solution.
If the profile curve is degree 3 then placing shape, or ‘around’ curves at the control point locations and lofting with the Loose style, will make a nice surface that matches the profile curve exactly. The key in getting something 'hard edged’and geometric like a filleted square to dissipate those corners nicely is to make sure the second curve in the loft is pretty close to the edge curve and is smooth - I used circles here - you can get away with that if you rebuild the loft with enough points - but that requires an extra control point in the profile curve to know where to place that circle, so add a knot to your profile curve to give it 5 points instead if four.
Starting curve, degree 2, arc:
Rebuild to degree 3, 4 pt
Notice that the second point inward is a little far from the outer curve - InsertKnot>Automatic or go back to the arc and rebuild to 5 points. (Degree 3)
Place curves, circles in this case, on each curve control point:
Loft (to the center point) all the closed curves.Line up the seams. Style = Loose.
Because we’re lofting curves with very disparate structures, use the Rebuild setting in Loft to make them compatible. This is a quick cheat, you could spend time making the curves compatible and much simpler…
In this file I added yet another knot and circle near the edge.
Pillowy.3dm (200.3 KB)