Can a 3D model of a copyrighted work be rendered legally without infringement?
First, copyright laws are complex and depend heavily on the specific details.  IMO, your question is really too broad to answer.

An interesting example of how details and interpretation affect whether something is a violation or not is Kienitz v Sconnie Nation.  In this case a copyrighted photo was clearly copied, modified, and used to make a t-shirt that was sold; but, it was not deemed a copyright violation.  On the surface it seems like a violation; but, the court ruled it was not a copyright violation because of the specific details of the case.  Using something as a starting point for a unique creative work that is clearly your own creation is not copying.  I am sure you can tell the difference.

Second, in your description you mention "Free Use".  If the owner has granted "Free Use" of their product; but, they are still wanting to declare the item copyrighted, I would hope that they have granted that "Free Use" under a defined agreement.  In that case, it would seem likely that the creator may just be trying to protect his design from being plagiarized and/or sold/used in a way that is against his intent.

If you have a way to contact the owner, why not just contact them and ask their permission for what you want to do.  If they have put it out for public use, they would probably be excited to have other people see their creation.  Just make sure they gets the credit for the design.  If it is a creation they are intending to protect (like Disney does with Mickey Mouse); then, the answer will be an unequivocal no.  Note that one weird exception is that Disney has granted use rights for Donald Duck to the University of Oregon "Ducks".

Finally, you state that that your intent is "for no purpose of using, distributing, creating, mixing, ..." and you list almost every way of making it public.  If your intent is for what you make/copy to never make it into the public domain; then, how will your question ever be anything other than hypothetical?  I know that there is presently no "private use" exclusion for copyrighted material.  It isn't legal to copy someone's DVD for you to watch privately; but, in reality, no one gets prosecuted for a single private instance.  It is abuse that gets prosecuted.

In what you intend, it would seem that you be best suited to seek out first what would be the "right" thing to do rather than just focusing on what would be "legal".  If you are concerned what you want to do may be wrong and/or illegal, it is probably best to not do it.