Hello MaximeJ,
I am very grateful for your investigation!
I am planning to use MPCORB database (https://minorplanetcenter.net/data) where JSON files contain keplerian elements. I will contact MPC and ask about the Frame.
Very clever idea with position/velocity initialization, now at least I know that this is not my code’s issue.
Thanks again, I will try to contribute to this community as much as I can.
Best Regards,
Piotr