template drop behaviour around sharp corners

In the past in these "bowtie" type of areas, I have addressed overlapping end conditions by placing an element that extends out from the vertex and targeting that. You can set a profile on that element to control elevation, similar to how a ditch or gore area would function. Not sure if this specifically addresses your issue, but thought I'd offer that method.

You could have a point control on that outer edge, but what else is that last bit of line controlled by otherwise.

As example...Simple template with 2-12' lanes, each sloping away from the centerline at 2%. You can even control the width with point controls along a feature. When you get to that corner, your centerline goes somewhere else. Even if you had the outer edge controlled by a point to a feature, there is no longer a centerline in that region to take the slopes from.

Actually, how would you define those elevations? Flat from the end of the alignment? Continuing the profile grade along the edge? How would that transition to where the outer edge "picked up" the centerline again?

Multilines are a very different, very old, 2D technology and there is very little design logic to them. A template is a complex design of relationships in 3D, so making that kind of (apparently) simple extrapolation really involved.