about zero-point energy
Here is an analogy. Consider a waterfall (or the drop of a river) generating power. When the water reaches the bottom of the ocean, you can't turn a waterwheel anymore, right?
But the water at the bottom of the deepest point in the ocean still has gravitational potential energy! It is feeling weight due to the Earth, and it's about 4000 miles from the center. In fact, since it only dropped 20 miles or so since it started in the mountains, it still has most of its potential energy untapped!
This is exactly the same concept. A potential is useless without a place to exploit the potential difference. There’s no drain at the bottom of the ocean; nor could there be since the Earth isn’t really a point mass at the center of its gravity field.
Running infinite debt
What you’re describing in the OP doesn’t seem to be anything like zero point energy, but is an observation that the total energy of the universe might be zero. How would that provide for infinite energy?
«Whatever energy you create could be balanced out by the gravitational energy it creates, yes?»
Yes. That is how the dark energy (if it's indeed the energy in empty space) is created as space expands. As I recall from Laurence Krauss’s book (IIRC the attribution), this is allowed because gravity has no fear of debt.
So can you do anything with that? Well… I don’t see anything. If you enlarge space you don’t get usable energy. Making use of gravity wells in the normal way, you will run out of stuff to throw into a black hole, and the potential is that of the event horizon, not infinite.
But consider this idea I came up with some time ago: imagine a future empty universe. Put two huge masses on opposite ends of a long string, and that string is so long that the expansion of space tries to carry them apart with more force than the gravitational attraction between them. The far end is essentially being lowered into an infinitely deep well, which is deeper than a black hole because you never reach the horizon.
In order for it to do work, you have to actually let it pull out more string. So this well is only infinite until you run out of string.
No matter how clever you are, there is still only a finite amount of useful potential up to your cosmic horizon.
beyond normal physics
Can they create new pocket universes? Can they create wormholes or acheive FTL travel? There may be unlimited energy sources there, too. Now you keep using energy until you “pollute” your own universe with too much entropy and reach limits there… so dump your waste into a parallel universe or through a wormhole beyond your cosmic horizon, or somesuch.