It appears that the vertical shift is caused by the fact that SLPK export is performed in WGS84 + EGM96 coordinate system, so the coordinates of the model are transformed accordingly. So can you please check that the altitude information for the reference points used in your project are defined in accordance to the chunk's coordinate system.
As far as I am aware, SLPK format is optimized for online viewers in order to display the data on the world's globe. So there do not seem to be any options for saving the data in other systems, but if you can provide any reference for such an option for SLPK we'll check that.