But how am I going to be hyperbombarded with ads during my favourite match of “Who’s The Best At Cheating”? Having to use an offshore DNS resolver just doesn’t feel right.

The EFF provides pretty sound advice, see the 2nd link in my initial comment.

One way of helping would be to tell people how to mitigate it. Telling them it’s impossible does the exact opposite.

They say it here, but I disagree. Fingerprinting is difficult to prevent but not impossible. Same thing as with malware: You’ll never be 100% protected from malware, but that doesn’t mean you shouldn’t take precautions against it, does it?

Here’s one way of testing how unique your fingerprint is.

Booting a live USB and reinstalling GRUB as follows has saved my butt in the past. Obviously replace the /dev/sdXY paths with your own. Further adjustments might be needed depending on your system.

# mount root partition:
sudo mount /dev/sdXY2 /mnt
# mount boot partition (if there is any)
sudo mount /dev/sdXY3 /mnt/boot
# mount efi partition (if there is any)
sudo mount /dev/sdXY1 /mnt/boot/efi
# mount other partitions:
for dir in /dev /dev/pts /proc /sys /sys/firmware/efi/efivars /run; do sudo mount --bind $dir /mnt$dir; done  
# chroot into mounted system:
sudo chroot /mnt /bin/bash -i 
# reinstall grub:
grub-install 
# rebuild grub.cfg:
update-grub 
# rebuild initramfs (not sure if necessary):
update-initramfs -u
# sync, exit chroot, reboot:
sync
exit
sudo reboot

Nice specs, nice setup. You might want to add another rainbow sticker or two, just in case :p