this thread is so long now, forgive me if someone had mentioned this idea, ...
but what about introducing (you might say re-introducing if you played ad&d 2nd ed) a simple weapons speed rule to give smaller weapons an edge. Nothing too complex. Say all one handed weapons get a +1 to initiative, light weapons +2. Any finessable weapons get an additional +1 (including two-handed war sword) which would make light weapons effectively +3. If dual weilding only the modifier for the larges/slowest weapon is used.
I don't have enough conan rp experience to be sure weather two-handed weapon damage should be reduced, but so far i agree with the arguements that they should not be changed. But I do think that faster movement with lighter weapons is a realistic factor that would make a real advantage for thier wielders. With lower hp and no magical healing, i think winning initiative in much more important than d&d. And it fits that zingarian dualer would have a good chance to step and strike the Hyborian hulk with the greatsword before he got the backswing raised.