Rather than resetting your entire browser to be in Private Browsing Mode, why not just set it to one tab? The Private Tab extension for Firefox adds private tabs to Firefox. This way, you can use the private browsing mode of Firefox in a single tab – while the rest of the browser stays un-private.
To use the add-on, all you need to do is click on the Firefox button and click on “New Private Tab”.
Now, when you view the private tab – you can tell it from the rest because it will have a dotted blue line under the page tab and will say (private tab) when you hover over it. I think this is a great idea and I do not see why Firefox refuses to do this by default.
You can pick up Private Tab from the Firefox Add-ons website.