Self-intersection when sweeping through spring endpoints

I have a spring-like structure made from a sweep of a circle cross section following the path of a helix. At the end of the spring, I want to extend its path so that its endpoint lies on the helix axis and its tangent is parallel to this axis. the radius of the spring itself is pretty large (larger than the radius of the helix), so most of my attempts have ended in self-intersections when calling opSweep(). I've been looking at splines (opFitSpline) being generated from the endpoint of the spring, the tangent of the endpoint for start tangent, some arbitrary point on the axis, and the direction of the axis for the end tangent. However, these only work for small radii.

I was wondering if anyone had an idea on how to create this spring with endpoints on its axis that takes into account its radius (i.e. some path as a function of the spring radius that connects the helix endpoint with its axis and allows for a circle sweep without self-intersections).

Thanks!