Given that what the countries in Europe used to do for the 2000 years prior was go to war with each other pretty much constantly, I'd say that the EU is working out very well indeed. It's far, far from perfect but given the alternative it's good enough and, given the enormity of the problem, good enough is a pretty overwhelming achievement.
I think that part of what makes the EU work is the ability and willingness to fudge things around the edges where no clear cut solution exists. That's why Norway is kind of in the EU and kind of not and why several countries can be in the EU without being in the Euro, and how you can deal with the whole Ireland/N.I. etc. It doesn't need to be perfect, just good enough to stop people from shooting at each other, and let us try to figure out the rest from there.
I'm not talking about overnight dissolution. I don't think that such a sudden and dramatic change would happen peacefully. Nor do I have the answers to your questions about whether a solution that fits around existing borders would work. I'm not an expert in any of this, it just seems to me that smaller countries more readily governable in a rational manner without resorting to Authoritarianism than larger ones.
As to whether any changes could be achieved without violence, yes, I 100% believe that. It might not seem evident to an outsider looking in at the politics of the place, but the overwhelming majority of people here are rational and just trying to go about their day. Nobody wants to be at war with their neighbours, and anyone trying to push for that is going to find themselves standing alone very fucking quickly.