How to make Firefox in normal mode work the same as in private browsing all the time?

I like always using Firefox in private browsing mode, but there are several issues which are kind of out of my control where other apps will open new Firefox windows, and the default behavior is to open them in non-private mode.

What can be done to make the normal mode operate exactly the same as private browsing mode (sans the purple mask icon in the window header)?

I've found info about launching Firefox with a "-private" flag but that is bugged in several ways, and it only helps if I use that shortcut. Other apps will still open new windows in non-private mode to congratulate me with a successful install or ask why I deleted them.

If you open the about:preferences page and select Privacy on the left, you can change History on the pull-down menu to Use custom settings for history. Once you do that, you can check the box that says Always use private browsing mode:

Navigate to about:preferences#privacy and under the History label select Never remember history:

This will have the same effect as always-private.

If you select Use custom settings for history there's also an explicit Always use private browsing mode checkbox, but I believe this has the same effect as Never remember history.