In the short term, it simply isn't going to happen. And attempting to hurry things along would only work against European interests. FIrst of all you'd exacerbate the divides, secondly you likely wouldn't actually see an end to NATO, but rather a rump, more hardline one with a shift in US military concentration eastwards. That would in turn make Russia EU relations worse and more unstable.

In the long term - who knows, maybe you'll get a Russian Willy Brandt and a shift in Russian public relations policy towards constant reassurance and apology for the past. That would eventually work, but I don't see it happening for the foreseeable future. Or perhaps over time the EU will be able to take the place of NATO in the minds of the Poles and Baltics, along with the military structures that implies, though without the Russian shift taking place, that wouldn't really change anything from an EU-RUssia perspective, except perhaps for the worse. And remember that NATO was a vital factor enabling the reconciliation and reintegration of Germany in Western Europe. (NATO's triple purpose: Keep the Russians out, the Americans in, and the Germans down.)

All in all, I don't quite get Europeans who are simultaneously pro EU integration, pro international stability, pro better EU-Russia relations, and anti-NATO. The last of these policy choices implies giving up on at least one of the first three.