Although it is true that there are a some reticulated irises that are sensitive to summer moisture, one of the main problems with growing reticulated irises isn't that the soil is too wet in summer, but rather that they break up into many small non flowering size bulbs quickly.
To my mind there is no easier cultivar to grow than 'Katharine Hodgkin' as it prefers to split into two flowering sized bulbs every year and thus can remain in the same spot a longer time. It is also very tolerant of summer moisture as long as the ground drains well. Only problem is that much of the commercial stock probably is virused, so one have to watch out for plants with striped flowers and removing them.
If you have heavy soil, try raised beds or planting close to a deciduous tree or a bush that sucks up excessive wet. Avoid summer irrigation as in planting annuals on top of bulbs.
