Forcing Vuze to Direct ALL Torrent Traffic Through PIA
I concluded the following about IP Binding for Vuze using PIA:
1. Launch Vuze
2. Go to Tools>Options
3. Click Connection (drop down arrow)>Advanced Network Settings
4. In the box that states Bind to Local IP type the code that has TAP ADAPTER next to it. This is the PIA TAP Adapter.
5. Scroll down and tick "Enforce IP bindings even when interfaces are not available".
6. Click Save
7. Re-launch Vuze
8. Load torrents
At the bottom right corner of the Vuze program, you will see ROUTING. Place your mouse cursor over it and wait for it to connect to PIA IPv4 address. It starts with 10. In case you're skeptical, you can go to Network and Sharing>Click on Local Area Connection link>Details. It will show you the IPv4 address that will match in Vuze.
All torrent traffic will be routed to PIA IPv4 address.
If the VPN disconnects, torrents will stop downloading immediately until the VPN re-establishes connection. Even if it looks like they are still connected to peers, they are dead.
You can also test it out by disconnecting the VPN manually (do not have internet browsers or Facebook Application open at the time) and go back to Vuze. Place your mouse cursor over ROUTING and you will see it is still connected to PIA IPv4 address. Eventually, the ROUTING button will turn red.
Hope this helps!!!

Comments
@Irr100
Your directions are too specific. Not everyone has the same exact hardware as you. I for instance have exactly two interfaces because I disabled everything I do not use. Saying eth4 is the one is the wrong way to say it. If a person uses "ipconfig /all" from an administrative command prompt, only one will show the words "TAP-Win32 Adapter V9". That is the interface to bind to your client of choice.
If you are downloading something you would not want the entire world to know about, you should do as @Irr100 says and *NEVER* deviate even for a moment. If you think the speeds are unacceptable, delete all infringing content and try a Linux ISO image with and without the VPN. What you are likely to see is that despite all evidence to the contrary, you can max out your speed regardless of if you use the VPN or not with them This means that the torrents you are downloading are not as well seeded as you thought.
And bear in mind that even if there were millions of seeds, you have no way to be certain any of them are real. Nor that they will bother to seed to you. There are too many variables to be sure what exactly is happening.
http://torrents.linuxmint.com/torrents/linuxmint-17.1-cinnamon-64bit.iso.torrent
And if you prefer a 32 bit or a different GUI version, here is the download link with all of them.
http://www.linuxmint.com/download.php
Have you considered it may be the region or server you are connecting to? For torrents, ping time is largely unimportant, so do not hesitate to connect to a distant region. It may be a lot faster than a local one.