Hi gentib,
The file in post #1 was smooth and can easily be used with a SubSurface Division. So I assume that is not your problem. I do not click on links I’m not familiar with, so I have sent you an upload link.
The only parts where I can see surface issues are with the Volume modeling.
Please have a look here:
https://www.amazon.com/clouddrive/share/jzqss01O1Y5BGVfQTJMHI2pt3b7ZMgaGN8bjkbbmpFw
There are two options to smooth Volume-based modeling. One is internally, and one is like post-processing for the overall model.
However, since it is based on a cubic base, the resulting mesh tries to interpolate among all these cubes. This means that there is a sweet spot among the settings, based on the targeted shape. A particular limitation is given. Please try to use a higher iteration. An example with the iteration set to 7 is here:
https://www.amazon.com/clouddrive/share/flHZ6ZaNpYB4ZQYiX2Y9dQDxzLv75TudkGotXiPrlfQ
https://help.maxon.net/us/index.html#OVOLUMEFILTER-ID_VOLUMEFILTER_FILTERTAB
I think the file from post #1 is perhaps the one you need.
Please use the upload link if you want me to look at your file. I’m happy to do so!
Cheers