BigSkyDog, welcome to the forum. You've come to the right place to get your question answered : )
I'm not one of the experts and I'm certain that you'll get a more thorough answer from one of them...but...
Me? I would pot them up earlier than June... I think I'd start potting them just as soon as they put on a little new growth. If you can't pot that many (and I couldn't), perhaps you can bareroot pack them. I kept a bag of iris bagged for about two weeks in the hottest part of the summer- I just watered them and kept them in the shade. I figured it was safer than actually planting them out.
Welcome to the club!
