I've been researching this topic for awhile now and have come across many conflicting answers. With it being too large to boil, what it comes down to is how long you're willing to wait...
I have been soaking a large root piece for months now and it's still floating and releasing tannins. I have another piece that has been “sun bathing” for just as long and is no closer to being tank ready than when I started with it.
Either way, it will take a very, very long time to cure without boiling. I've managed to cure small pieces with boiling in under a month easily; typically within two weeks. You may be better off searching for bogwood that has already soaked for ages or driftwood that has already been sun bleached. If you're willing to wait for these pieces you have to cure, just note that it may take many months or even years depending on how green they really are. If they're not too green, I would suggest soaking them in water with 1tsp of aquarium salt per gallon until all or most of the tannins have been released. The salt helps release the tannins quicker as well as help sterilize the wood. Then, soak it without the salt for an additional week to remove the salt from it.
Edit: I forgot to mention that the root may still float (most likely) once it stops releasing tannins. This is fine. Just make sure there is no bark on it and you do a nice soft sanding on it, rinse it well, and then you can hold it down in your tank with heavy rocks (use zipties if necessary).