Can you find the route of the existing 12/3 underground branch circuit cable? If so, you can expose the 12/3 cable in its trench and lay a 12/2 cable alongside it to carry the neutral and grounding conductors as per NEC 300.5(I):
(I) Conductors of the Same Circuit. All conductors of the same circuit and, where used, the grounded conductor and all equipment grounding conductors shall be installed in the same raceway or cable or shall be installed in close proximity in the same trench.
From here, you can use the 12/2 cable's neutral and ground conductors to provide neutral and ground to the garage light without causing the current loop/fault path problems that reusing the garage's neutral conductor does. The original setup was bodged in using the garage's neutral, by the way, and is likely a California-style or Carter-style three-way; you'll have to check which one, though, and rewire it to the California style if it is currently a Carter-style setup. For those who don't see the alternative three-way styles: Carter-style three-way switches the hot and neutral of the lamp(s) and is considered unsafe for that reason, while a California-style three way switch connects all three terminals of the three-way switches together to produce a setup where both the switched and unswitched hots are available at each switch.
EDIT: didn't see that the driveway was in the way -- replacing the 12/3 isn't an option anyway, as you'd need 12/4 + ground cable, and as far as I know, such a thing is not made in UF, as 3-phase applications are typically wired in conduit. Since it is blacktop, you could break up the section running over the cable-trench then lay down a cold mix patch once the trench is backfilled...
Also, is this really Romex/NM? That stuff is NOT rated for direct burial! Or is this a UF-type cable that is direct bury rated?