Max...
A friend of mine used to say there's no substitute for cubic inches when it comes to engines, and with flash units and trying to overpower the afternoon sun, there's no substitute for watt seconds.
Especially if you want the light to be modified in a very flattering way.
The 580s are pretty nice, but they're actually pretty small power wise when it comes to high noon light. You could use them directly and it will probably work, but I don't think it would look quite as nice as a studio flash on location powered by a battery or a dedicated battery pack system such as the Profoto 7b or the Elinchrom Ranger.
Check out this product:
http://www.innovatronix.com/compatib.asp
This inverter/battery will power a lot of monoblocs and the price is right...You'd be able to drive a 600 watt second elinchrom style or style s through a large softbox and probably get about f16 out of it at 100 ISO...
If you use a 5d, lets say that the main exposure (ambient @ 100 ISO) is 1/200th at f11, then f16 will make your background one stop darker than the main...you might even be able to get more power out of the flash, but figure you'll need at least a 600 w/s unit to get enough power to drive a light into a nice large light source to create a cool quality of light--and give you that aperture...note: it will not work with the rx series of elinchrom strobe units but the older, monoblocs, it will.
The later in the day, the less need for power as your ambient light levels are dropping, so you might even be able to accomplish this with a 580 into a small box, but for high noon kind of lighting, you'll need power...
Paul