The image you showed is the back - does the front look the same? I can’t think of any reason that an imported file would behave differently than a file in LightBurn. If it looks right in the preview, that’s the data being sent to the laser.
I took a quick look at the files you submitted, and I don’t see anything strange in the settings, but I did notice something about the file - it’s piecemeal, not continuous shapes in most of it:
If you ungroup the file content, very little of it is continuous shapes, and that’s going to affect the path planning. If the machine is skipping steps anywhere, it might be that the ends don’t line up because of this.
Run the auto-join tool to reconnect it all, and see if that helps. Ungroup everything, select it all, Edit > Auto Join selected shapes (or just Alt-J).
If that doesn’t help, then can you export a small section of the cut, like this piece:
Import that as an AI in LightBurn and in RDWorks, and use each program to produce a machine file? In LightBurn you use “Save RD File” and in RDWorks it’s “Output UFile” I think, but the buttons are nearly in the same spot. Send both files to me so I can check them for differences. If you can actually run them to verify that the machine output is different that would be good.