Welcome to the Core and Happy Christmas !
I fully sympathize - I can never fully 'get' the behaviour of those clamp constraints, and they never seem to do exactly what I want, so I am the wrong person to advise on use of those. But I can recommend a different way, depending on what you need.
One very simple way to get a straight spline between 2 things that move is to position 2 'target' Nulls at the connection points of / as children of your main objects, then use the Tracer to 'connect all nodes' which will constantly draw a straight spline between them.
If you want to try simulation then Rope Belt is probably the way to go, but I would tend to avoid that approach, as it is quite difficult to art direct 'tension' using that and things have a tendency to be very 'floppy'.
CBR