One aspect of fingerprinting that I did not understand before looking into this a couple of years back is that the first time you run firefox (and quite likely other browsers as well) it generates a random ID and uses that particular ID every time thereafter. That ID alone is enough to fingerprint you; and the only way to get rid of it is to reinstall firefox.
If you can set firefox up to run in a disposable, and NEVER run it in the disposable template, then every time you fire it up it’s as if it is a clean install and you get a different random number ID. The problem then is that it’s going to be completely uncustomized. With firefox, however, you can “arkenfox” it…and that involves a lot of pre-configuring; you can set all sorts of things (right down to getting rid of the obnoxious search-from-the-address-bar which in addition to being annoying since it searches for sites instead of taking you to them, is just a way for google to spy on you) before you open the browser for the first time. [Guide] Automatically install extensions and configure new (dispvm) hardened Firefox profiles with arkenfox user.js and policies