Provided the threads are still ok you should be fine using the same side of the hub, get yourself a decent lockring tool and do it properly. I use this one from Velosolo http://velosolo.com/combiwhip.html.
Have you tried tightening up the sprocket? if that has slipped back it will be forced against the lockring making it seem tight when its not, tighten up the sprocket then try tighten up the lockring some more.
Provided the threads are still ok you should be fine using the same side of the hub, get yourself a decent lockring tool and do it properly. I use this one from Velosolo http://velosolo.com/combiwhip.html.
Have you tried tightening up the sprocket? if that has slipped back it will be forced against the lockring making it seem tight when its not, tighten up the sprocket then try tighten up the lockring some more.