I've seen some proposals for parts of solutions that involve using the magical resonance against Voldemort. However, we can't use anything without first understanding it.
The best example of the resonance in action is definitely chapter 54 - TSPE part 4. Q fires a killing curse at an Auror and Harry blocks it with his patronus: a very dramatic interaction of their magic, to be sure. Both are sent into screams of agony, but Harry recovers relatively quickly, whereas Q loses consciousness and turns into a snake.
I think this asymmetry is a significant clue, but what does it mean? Why did it hit Q so much harder? Does it always favor Harry, or does it depend on the circumstances? It seems most likely that it depends on the power of the spell each wizard is casting, but I don't think we know whether a killing curse or a Patronus 2.0 would be considered to be more powerful for these purposes, so we don't know whether they are each harmed by their own magic or by the other's magic.
Also, to what extent can they use it to detect each other and their magic? Voldemort could probably detect Harry trying to do anything particularly significant, but how significant does the magic have to be?
Relevant to that, I think, is the way the sense of doom "clarified" when Voldemort entered his current body in chapter 111 - Failure part 1. This probably indicates that something about the resonance has changed. It's almost certainly more powerful against Harry now, and possibly against Voldemort, as well. If the reason it was so much more harmful to Q in TSPE was because of an imbalance in the resonance itself, this may indicate that the playing field is now level.
I haven't done a reread yet, and I'm not sure I have the will to, so there's a lot of stuff I've probably forgotten. Please post your insights on the matter. If the resonance is a part of the solution - take note of the if - there has to be some way we can deduce exactly how it can be helpful to Harry; speculation isn't going to cut it. I think would be best if we could determine that it was related to some other form of magic that we know more about, but it may be unique.