Importing mocap data on existing mesh

I have a CSV with XYZ coordinates of 14 joints of a human changing over a time period. I created a script to import these data as empties and create an armature that is parented to the empties. This allows me to visualize the movement on the armature.
What I would like to do next is to visualize this movement on a human mesh. Since I have a lot of CSV data to visualize I need to make this as easy and automated as possible. That’s why I’m thinking about a “start blender file” that will have a pre-rigged human mesh with the armature parented to the empties that match the joints from CSV. Then I will use a script to keyframe the empties to the data from CSV.
This approach works okayish but the resulting human mesh animation is a bit skewed in proportions (see 2nd pic) - I guess this is because the initial distances between the empties are different than those that are in the CSV data and can be fixed.
I’m wondering if this is the right approach to do this and I’d appreciate any tip on how to make this better.
Here is the Blender file and the animation:
https://drive.google.com/drive/folders/1A2xeLEEf0m-Oh2MO4Rbzrm9mWKf8SJ2g?usp=sharing