Okay - I was able to resolve the issue...the only problem is, I don't know the reason why it worked (for this reason, I'm considering the effort as a partial fail):
I fully removed all tor installs, then rebooted the system. Once I did that, I downloaded the tar package, checked .sig, and unzipped the file - all under my profile.
I then performed the dnf update and dnf upgrade -y. Once that was performed, I was able to move the directory from my home directory to the /usr/local/share directory (which was accepted under my regular user profile).
Once that was completed, I was able to successfully perform the --register-app command under my regular profile. (Positive benefit to this is now I know that that command works on other programs.)
I'll create another user profile later to fully test the functionality, as I have been working on this for the past four hours. Once I confirm functionality there, I'll move the folder to the /opt directory (still unsure of why the documentation mentions to place it in /usr/local/share, if everyone here recommends to move it to /opt shrugs), and create the link to the /usr/local/share/ directory.
(A question, upon that last sentence: should I create another folder in the /usr/local/share for the tor link?)
In any case, thanks to everyone for your help so far!