OP, looks like your trip is perfectly suited for the distance-based Asiana (OZ) award chart.

Here is a typical routing for your trip:

LAX-FRA-MAD
(open jaw)
BCN-ATH
ATH-FRA-LAX

Which comes at 14781 flying miles, and will price out as 78K OZ miles per person in economy. In fact, your BCN-ATH is going to be free, because adding it doesn't cause you jump to a higher mileage level.

Stopover duration is not limited, as long as your ticket is valid. In addition to 5 stopovers, the OZ rules also allow for 1 open jaw, which you can use in your MAD-BCN segment.

You can see more of the rules here: http://us.flyasiana.com/Global/US/en...?fid=CLUB16210

Since you are already using Award Nexus, I suggest you use the Route Explorer tool to figure out routes for your segments (LAX-MAD, BCN-ATH, and ATH-LAX) and also the Distance Pricer to price out the routes found by the Route Explorer.

Once you have researched your desired routes, then you can start searching for awards for those route segments.