The Live Soap goal is the one which will give an actual minimal surface, since the shape does not depend on the initial meshing, and the forces are based on the triangle areas, not just the edges.
The EdgeLengths component is simply a convenient way of creating Length(spring) goals, so these two are the same.
While these edge based goals will not give you a minimal surface, that doesn’t necessarily mean the resulting surface cannot be used for a tensile structure. In fact, many built tensile membrane structures are not in the shape of minimal surfaces. It is important that all parts of the fabric are in tension, but having different magnitudes of tension depending on direction is not itself a problem, and it does allow more freedom in choosing the shape. Strictly minimal surfaces (equal tension in all directions, zero mean curvature, as approximated by soap films) are of interest in mathematics though.
Bear in mind when finding tensile shapes with springs that the ratio of U to V divisions will affect the shape, and using a boundary aligned vs diagonal grid will give different results.
I don’t think it makes much sense to use constant tension goals in this way. They can be useful for designing cable net structures though.
There is no need for any timer component. Kangaroo2 does the iteration automatically.
The regular ‘Solver’ component is the one I’d recommend using most of the time rather than the bouncy one, since it converges quicker, and gives you structured data output.
You can set the Anchor strength to 1e300 to make sure they do not move at all.
There should be no need to change the strength of the tension goals here, since the resulting geometry is the same if you are finding the form with no other forces acting. You can just leave them at their default values.