Bringing a Surface to a Point

I have several cases where need to fill gaps in a surface that come to a point.

However, always get bulges as the shape moves to the point, whether I use networksrf or sweep2.

That curve is the end of the object. It has to be perfectly straight. I’ve tried extending splines over the sharp curve, create a surface, and trim—but there are always bulges away from the curve.

If I use patch, I can avoid the lump (illustrating it is possible) but I cannot get a smooth transition to the surrounding surfaces.

I generalize the question:

Is there any way to create two surfaces tangent where at, one edge, the surfaces are at right angles?

In other words have a variable radius ?

Here is a perspective view. If the end did not come to a point, tangency would be an imposibility while filling this area.

can you post a Rhino file? maybe you need to overbuild the surface and trim it.