I'm not sure you can. In addition to being completely flat light, there is a crispness to the image that I think can only come from a true ringflash because the lightsource is a narrow light tube. If you used a whole ring of softboxes, you would get flat, but not crisp. The homemade flourescent rig that Jerry Avenaim uses (and Rolando likes) does a good simulation because the tubes are, again, narrow lightsources and therefore give some sort of an edge to the light, and make a complete, viewable shadow. This is used with hot lights in commercials for cosmetics and Victoria's Secret, but if you get a behind-the-scenes look at the rig they use, they have still maintained a narrow lightsouce. No matter the diameter of the circle, the lightsource itself is still relatively narrow (narrow flashtube, narrow flourescemt tubes) as opposed to the broader light put out by a group of softboxes.
There are some that are small and run off battery packs and screw into your lense where the filters go. You might look on Ebay, or a rent one from pro-rental house to find one for this shoot and see if you like it. Here's a sample of true ringflash, note the crispness and the shadows all the way around: (model is Amber Marie).
Andy Pearlman Studio