Is it possible to drill into the binding disc to expand one of the holes so it will fit with the 3D set up? Or would that compromise the strength of the binding plate and the weight distribution?
I think you're overthinking your solution. Assuming you could drill those holes without cracking the baseplate do you really want to ride such a ghetto setup? APart from how it'll look, it'll never be precise enough to fit -well-. You dont need to do that to yourself.
I'm assuming that you're willing to bust out the power tools to mod a $3 piece of plastic because money is tight. No one here is gonna give you grief for being on a tight budget, least of all me.
Here's a better way to approach this problem: Do you have access to a ski shop? Is there one within 30 miles of where you live? If the answer is yes, grab those bindings (and the board if you're feeling adventurous) and drive over there. If you dont have a car, call one of your friends.
If you can't get to a ski shop, call Burton Rider Services and ask for help. Talk to the person that answers the phone like he's a real person and be cool. Believe it or not, the people I've spoken to act like they work at a local shop. They're nice, they know how to ride and they actually want to help people love the sport.
Whether you call Burton or hit up a local spot, the parts you need costs less then $10. If you're cool, you might even get an old pair of baseplates they have laying around for free.