Hello @mendler,
Your base level topology is not of sufficient quality to get great results in ZBrush when subdividing, sculpting, or projecting. Ideal topology for best results doing these things in ZBrush is well distributed quad topology, as close to square-shaped as possible. This mesh has already been optimized and output as a low poly asset. You have long, stretched triangular topology which will cause distortion with many processes in ZBrush. Unfortunately, the UVs are tied to this topology.
You can try disabling the SMT (subdivision smoothing) button in the Geometry palette when subdividing. This will subdivide the mesh without any smoothing applied, and produce a more faceted looking version of the high poly model similar to the low poly version but with a higher polycount. Doing so may avoid some of the distortion.
Otherwise, unless you have access to an earlier version of the model while it still had quad topology, you may need to do some touch-up. Duplicate the mesh and retopologize it with ZRemesher. This will create a low poly quad topology version of the mesh with topology adequate for sculpting and projection. Subdivide the new mesh and project the high res detail from the original mesh onto the new using the process described on this page.
Now the detail will have been transferred to a multi-res mesh with clean quad topology which will produce much better sculpting results. Unfortunately, any distorted areas will have come with it. You can spot touch up those areas using the normal ZBrush toolset, or brushes like the XTractor brush which can function like a clone brush to copy detail from non-distorted areas of the mesh to cover up the distorted ones, textured alpha brushes, or the pattern brushes.
Once you have more satisfactory results, since print output is your goal you can use Decimation Master to again decimate the geometry back into a medium resolution mesh that should have a polycount accessible to most slicing programs while still keeping most of the detail intact.
Good luck!