As a work around if you are running on MacOS or GNU/LINUX you could give this wrapper script a try.
You may access help by running the script with the help argument :
eg 
chmod 755 /path/to/start-private-browser.bash
/path/to/start-private-browser.bash --help
What this script is doing is starting up a version of brave which stores the data in a different place each time it is called. This lets you start as many separate instances of brave as you like.
Then when you close the last window all the data from that session is also deleted.
Maybe it helps you out in the mean time. Fingers crossed.