Hmmm... I'm not sure this is going to work. It does fix the normals flipping, but as the profile rotates, so does the extruded shape and the rotation can get pretty extreme, so it creates some weird shakiness to the motion. I played briefly with parenting the profile to another control curve, which takes the expression, freeing the profile itself to be rotated just in the y axis to counteract this rotation, but I don't know how to compute what that counter-rotation might be.

I might have to look at something completely outside the extrude function.