Installing Acquia BLT on an existing site
You have two distinct problems here:

&quot;Composerizing&quot; your codebase
Installing BLT

The latter should be pretty painless once you've got the former (theoretically more painful) out of the way.
Fortunately, the Composerize Drupal plugin should get you most if not all of the way there. From the description of your project, you'll want to run this in the root folder (the one containing config/ and docroot/). You don't need to move anything out of the docroot/ folder yourself, anything that needs to be updated will be.
Once that process is complete, run database updates (contrib modules may have been updated to more recent versions), clear cache, verify the site is working, and commit the changes.
At this point you have the structure BLT is expecting, so following the installation instructions again (link in your third approach) should work out a bit better.