You know what they say about hacking e-readers: good things happen to those who are brave enough to try it. Hacking and rooting Android tablets is not really that hard. There are plenty of solutions and guides available for that. How about the Kindle Paperwhite 2? User yossarian17 @ MobileRead has posted a script that lets you jailbreak your Kindle Paperwhite 2. The script can be used to open a root shell, run an arbitrary script, or install jailbreak solutions.
Unlike Android tablets, I am not sure jailbreaking a Kindle Paperwhite is for everyone. If you enjoy hacking Linux based systems, you may want to give this a try. The appropriate package can be downloaded here.