Do you want to try ArchLinuxARM?
It's based off of a rolling-release distro, so it's always up-to-date.
Bleeding-edge, in fact.
Here is a direct link to their package archives showing the available version of calibre:
http://archlinuxarm.org/packages?search=calibre
Yes, I use ArchLinux on my PC.
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Just because Raspbian is the most famous ARM distro, doesn't mean you have to use it. Personally, I've given up on Debian and derivatives.