Oh, it's (re)randomised upon each restart, whew, thanks for the heads up
edit: er, I think that that also suggests that I need to restart firefox more often...
Doing it on restart makes the mitigation de facto useless. How often do you have 10, 20, 30d (or even longer) desktop uptime these days? And no one is regularly restarting their core applications when their desktop is still up.
Enjoy the fingerprinting.
The webpage would have to scan the entire UUID space to create this fingerprint, which seems unlikely.