Alignment of Teeth Along Curve and Animating Movement

I am working on a small project that involves drawing a curve over a set of misaligned teeth then aligning them accurately along the curve. So far I have only managed to segment the teeth but having a challenge tracing the curve over the teeth from a reference image then moving the teeth to their final position. After the above task, I would like to animate the object showing the movement.

This is a screenshot of the initial setup with the crooked upper teeth:

The teeth alignment is guided using this reference chart:

The teeth alignment is guided by overlaying a reference curve of similar scale to the stl like this screenshot shows:

This is a screenshot of the intended setup:

This is a quick video of the animation after:

Here is the stl file of the segmented teeth that I started on:

Essentially I am looking for an add-on to do the above since it is a repetitive process with little modelling required. The most important part is the controls for moving the individual teeth : moving the tooth up/down/left/right and rotating it.

Budget : $100 - 200 USD