Google Chrome for Android includes a feature called [incognito mode](http://en.wikipedia.org/wiki/Privacy_mode). This feature, when I activate it, is designed to help prevent Chrome from automatically remembering and storing information about which websites I've visited in the past.

I've installed the free version of [Qustodio](https://play.google.com/store/apps/details?id=com.qustodio.qustodioapp&hl=en) (a Web filtering app) on my Android device. Unfortunately, as soon as the user enters incognito mode, Qustodio for Android stops working.

What are my options?  Well:


*  I could do the following procedure:
    1.  Install a browser without private browsing, such as [Zirco Browser](http://play.google.com/store/apps/details?id=org.zirco), Ranger, Mobicip, or Kiddoware Kids Safe. (Note: These types of browsers tend to rely on the system "WebView" component. Make sure to run Android 5.0 or better so that you can download [WebView security updates](https://play.google.com/store/apps/details?id=com.google.android.webview&hl=en) from the Google Play store.  These security updates may help keep hackers from breaking into your device.)
    2.  Configure [Smart App Lock](http://play.google.com/store/apps/details?id=com.sp.protector.free) or similar to prevent use of other browsers.
    3.  Optionally, install [the free version of NetAddictFree](http://bit.ly/1NrDlG5), which can mail out Zirco's history logs to an accountability partner.

I would do the above procedure, except for the following: I'm running an old Android version. For me to upgrade to a newer Android version, I'd have to switch to a third-party ROM, and this would be a hassle.

*  I could spend money on a more-powerful filter, such as NetSpark or Livigent.  But I'd rather not spend any money.

*  I could [contact Qustodio's support team](https://www.qustodio.com/en/help/) and send in a bug report.  But I don't want to bother.

*  I could uninstall Qustodio, could install Norton Family, and could try Norton Family's incognito-detection feature.  But I don't want to bother doing that either.

On desktop OSes, I already know that it's possible to disable Google Chrome's incognito mode.  But I also use Android.  How can I disable Google Chrome's incognito mode on my Android device?

Please assume the following:

* I always run the latest version of Android.

* My device is owned and controlled by me. It is **not** administered by a Google Apps domain administrator at my workplace or my school. And so I cannot [use the Google Apps admin console to disable incognito mode](https://support.google.com/chrome/a/answer/2657289?hl=en). (I also don't want to pay a fee in order to sign up for Google Apps for Work.)

* I am willing to root my device.

(**Note to readers:** Please remember that, even if you disable Google Chrome's incognito mode, there are other ways for device users to browse the Web without leaving any tracks.)

<sub>I thank Android.SE user [Lucky](http://android.stackexchange.com/users/27149/lucky) for inspiring this question.</sub>