This is a fascinating idea.
It makes sense that the "source" of the (possibly phantom) sound could be anywhere in the signal chain, from actual stimulation in the cochlea to processing errors in the brain itself. But regardless of the "source", the real question is how would the brain interpret the superposition of a cancelling signal? We understand that acoustic mixing could cancel an actual sound at the eardrum... but electrical cancellation is also a real thing, and once a "signal" makes it to the brain why would the brain magically interpret two different signals differently? So what if one started out as "real" (externally acoustic) while the other started out as "fake" (undesirable stimulation of the cochlea, or even a flaw within the brain). Once both "signals" are within the auditory processing centers they are just that - signals - and aren't tagged as "real" and "fake".
Yes, syncing up the frequency and phase could be challenging. But I'll venture out on this limb a ways with another idea: Biofeedback. There are countless examples of the brain adapting to accommodate things. Some are natural (did you know that each person's neural network is unique, and that an infant's brain learns to map theirs?) while others are external/artificial (such as learning to modulate one's own heartbeat and blood pressure). I wonder if a closed loop system could be created whereby the brain modulates the frequency and phase to minimize the effect of tinnitus. There's an obvious error signal available, and an obvious result of improved control available, so in theory it's possible. Might take time but so does learning to walk with a prosthetic that is controlled by nerve impulses.
Again, a fascinating idea.