Not being a Time Machine aficionado (or even user), but having tried to digest this thread, my best guess is that the only way you can do what you want to do is by partitioning your 3Tb HD, archiving everything that isn't currently important on a really large partition, and keeping your current stuff, the stuff that needs to be TM'ed, on a partition that is small enough for you to work with.
But remember that you'll still need your backup HD to be no less than a Tb, and also remember that, in addition, you'll probably need to reformat your HD.