I have some iris that need to be moved: some for aesthetic reasons, some because they are not happy where they are, some that need dividing, and some where rhizomes are sticking straight up in the air because of too much rain and heavy stalks. July is miserable weather. Additionally July/August is when new iris arrive. Established iris are really hard to dig up and divide because the ground is so hard by then. And ... I am always really stressed by all the iris tasks at this time. It is the one time of the year when I do not enjoy gardening.

Can I move them earlier as in now when it easier and less stressful to work in the garden?

Additionally where rhizomes are sticking up in air, how do I reorient them if foliage has adjusted to that angle?

You can move them at any time. It is best to wait until after they bloom but if they need to move it won't hurt them. I had one die and because I was supposed to have a garden tour I popped another iris out of a pot and into it's spot in early March (thought fans would look better than an empty space). It was happy with it's new home and bloomed. You should be past hard freezes by now so May and June would be great planting times.