Here you will enter the IP address of the interface you want to use. Simply rename the item key to BindAddressIPv4 (case matters!) and press Tab to jump over to the Value field. Simply click on the Add Child button which will create a New Item entry. When Property List Editor opens the plist file, it should have the Root dictionary selected. Either open it directly or right click on the plist file and choose Open With and Property List Editor should be an option. If you have the DevTools, Property List Editor is located at /Developer/Applications/Utilities/Property List Editor. You might want to make a backup copy of it before you start messing around with it. The plist file is located at ~/Library/Preferences/. You can either edit the plist file using the Property List Editor program, if you have the Apple Developer's Tools package (aka XCode and friends) installed, or Terminal command line using the defaults command. Transmission saves to it on quit so any changes you make while it is open will be overwritten.
So, how do you do it? First, quit Transmission as you don't want to edit the config file while it is running. Adding the properly named option and the IP address of my VPN, Transmission properly bound to that network and all traffic is going over it!
After a long time digging thru the source code (thanks for making that available!), I found the section that loads the plist file and saw that the Mac GUI option has a slightly different option spelling of BindAddressIPv4. I tried entering this option within the preferences plist file but it still didn't work. The wiki mentions using a 'bind-address-ipv4' option to have Transmission bind to a specific IP address of a network interface. I wanted to configure Transmission to use a specific network interface, specifically a secure VPN connection, but the Mac GUI doesn't have such an option within the preferences.