The way I think about this is that all the variants logically represent the same physical item so in terms of inventory tracking only the first one (I call it the "master") needs to be accurate. For the other 2 you can set the inventory tracking policy to "Do Not Track".
Assuming you set up tracking per above you'd need 2 sync tasks: Var 2 -> Var 1 and Var 3 -> Var 1. Basically you would be ensuring orders containing the other variants will update Var 1.
The next thing to cover is the out of stock scenario. We provide a script that enhances the standard Shopify option_selection.js functionality that most themes use to update prices and the add to cart button state based on the inventory. So when the customer chooses Var 2 it really uses the inventory of Var 1 to figure out if the product is out of stock (since Var 1 is the master). This script can be modified to account for the backorder concept you mentioned earlier.
I'd be happy to set this up for you if you want to experiment with the App.
Thanks, Gavin.