Well I thought I would ask someone who hybridizes those big old flounces and poms - the Jedlickas (owners of Blue J). Kathy Jedlicka was kind enough to respond (and sent me pics of some of their space-age seedlings!!! They have a flattie with flounces that I find really cool).
Here is a bit of what she wrote:
"Normally the first flowers to open on a stalk will have the best Appendages (horns, spoons, flounces and now pom poms.)
Tilling over the roots, along with low of fertilizer, water and sunlight will harm the appendage.
Full sun, good water drainage and not too much nitrogen or water will make the best results.
Also if the clump is divided and moved about every 4 years to soil that has never had iris before, that really helps the spoons and flounces." *
* I found this interesting because it is also what you do with Japanese iris.