If I may offer a suggestion, I'd try to parameterize bezier curves based on the circle tangets: https://imgur.com/joLcm2w (red fixed/calculated, blue adjustable)

Thanks, that's an interesting approach. Let me play with that :)

Another option would be tangent circle arcs. These might be easier to handle (path-wise) once you have the math down: https://imgur.com/p546ref