Even if you magically had your own DSN, would anyone but NASA even know exactly where they are with enough precision to communicate with them? In a way, that's now your layer 1 authentication key. The coordinates of where to "point" your DSN.
Even if not, it should be fairly straightforward to compute its position from the initial flightplan. Once it escaped Jupiter its trajectory is just a straight line.
I honestly don't know that we understand gravity well enough to keep this close of track of this small of an object for so long. Plus all the effects of the "negligible" gravities of nearby objects have to add up over time, and we can only include so many bodies in our N-bodies simulation, right?