Ubuntu – Tor Browser Bundle’s version of Firefox [Tor Browser] is recognized as the main Firefox installation [Ubuntu 12.04]

I cannot vouch for the safety (in terms of Tor's purposes and goals) of the next solution, but this is what I did in my own case.

I suppose that you already have tor browser registered as an app in your system, but if you don't than run this command from the directory containing the unpacked stuff, it must be something like:

~/tor-browser_en-US

And run this command:

~/tor-browser_en-US$ ./start-tor-browser.desktop --register-app

Then the solution itself. You should have a launcher file ~/.local/share/applications/start-tor-browser.desktop file. Drag it to your launcher bar. And in the file itself change the line:

Exec=sh -c '"/home/<username>/tor-browser_en-US/Browser/start-tor-browser" --detach || ([ !  -x "/home/<username>/tor-browser_en-US/Browser/start-tor-browser" ] && "$(dirname "$*")"/Browser/start-tor-browser --detach)' dummy %k

to this one (with substitution of the username properly):

Exec=/home/<username>/tor-browser_en-US/Browser/start-tor-browser

That is make it to call the executable directly, not via a shell.

That's it, but I would like to repeat that I'm not sure how these changes affect the abilities of Tor browser. I suppose that nothing harmful was done.

The thing that hangs is gpg. Run ps -ef | grep gpg while tor is verifying signatures and see there's actually a gpg running.
Tor browser installer will run gpg --refresh-keys anyways, so (from here)

Because of some jerk on the internet poisoning PGP keys, downloading and using the TB developers' poisoned key will take forever

But we don't need to follow the link to cure the gpg db, as it has another home directory. We just need to download and install the 'poisoned' key safely.
This thing is implemented in gpg 2.2.17 and later versions. So you need to /usr/bin/gpg --version and update gpg if it's older than 2.2.17.
The update process is rather simple, too: get to this git gist, load the script, replace 2.2.10 with 2.2.17 within the script and run download, compilation and make.
Maybe you should copy /usr/local/bin/gpg* over /usr/bin/gpg* after it.
Enjoy )

gpg (GnuPG) 2.2.17
libgcrypt 1.8.3
Copyright (C) 2019 Free Software Foundation, Inc.