Transform the map frame into custom global coordinate system

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I'm running RTABMap and mapping is working correctly with Lidar, odometry and RGBD sensor data. In order to overlay the generated map with a CAD model, I need to transform the map frame into the CAD models/lab environments custom coordinate system.
I'm using Apriltag markers with known (a priori) coordinates relative to the custom coordinate system and detect them while mapping. The translation part of the transformation from map_frame to my custom coordinate system origin is working fine with the help of Marker/Priors in RTABMap (see original question here). See this for the documentation regarding the parameter in RTABMap. Basically what this param does is, that one can input global coordinates and RTABMap will translate the map_frame according to the local tag detection coordinates and their corresponding global coordinates. Unfortunately, Marker/Priors will not rotate the map_frame into my custom coordinate system, because this is breaking REP105/3 by using custom coordinate systems instead of ROS coordinate system definitions and that's why it is not supported in RTABMap.

Is there a way to add the correct rotation manually while or after mapping by checking for the map_frame orientation and comparing the differences to the fixed custom coordinate system and then applying the right rotation angles?

Or, can I guarantee by modifying the map_framethat a fixed coordinate direction related to my environment is always present in the map_frame, based on the cardinal directions or other constraints? Normally, the direction and origin of the ROS coordinate frame is dependend on the starting angle/direction of the camera.
A small example, I want to achieve that the x-axis always points to the north, y always points to the east etc. while or after the mapping process. This would help, because I would just need to rotate axes in a static transform, because the rotation would be constant with this solution for every scan I do.
For better visualization, I quote this comment from https://answers.ros.org/question/3820...:

If you build a map with rtabmap and save it, you can then calculate the static rotation needed based on where the map x-axis ended up. Doing this dynamically is more difficult: you will need to read the initial magnetic orientation of the robot once before you begin the rtabmap mapping procedure.

I've tried to find out how I can implement it this way by asking the following question under the above mentioned answers.ros post:

Can you explain to me how to calculate the static rotation from RTABMap map_frame to my own custom coordinate system? How do I find out, where the axes of the ROS coordinate system point to after running rtabmap and/or dynamically and how much I need to rotate it to fit my custom coordinate system?
The translation part is already working inside RTABMap with the help of Marker/Priors parameter by setting global coordinates for the known accurate positions of the markers and detecting exactly these markers in local coordinates ...