I have several kinds of iris from huge bearded to dwarf. None of them are planted deep (and they almost never get fertilized, lol). They all do better in dry soil close to the surface, and the less I dig them up, the more they crowd, the better they seem to like it.

Some even bloom in the winter - the big bearded ones. I'd ask at a local nursery - not a big box store - for help, if you need it. I'm in zone 4-5, so what works here may not work for you.