Thanks for the feedback.
I hope the provided material allows for something you can work with.
I worked on the XPresso-based file, as constraining IK is a little bit uncomfortable for me 😉
I put a request in to have that three points in space into a connecting Circle.
With the three single-axis rotation arms, we get a triangle in space, which could be expressed with a radius-changing circle. Below that circle is in its middle point perpendicular down the moving object (printing or operating head), as the three "legs" are fixed in length.
Enjoy your project