Welcome!
As already noted, irises are a hardy flower. I have had good success with digging up clumps and directly placing them on top of the soil after removing the sod. This late in the season I'd remove a small depth, put them down, then put the removed soil on top of the exposed roots. Crowd them as they won't be there permanently. Of course you could do the beds in stages, half each year, with the crowding in the half not being worked on immediately, then repeat on other half.
The other option is the potted option, which I have never had luck with, so others can give you ideas on that and many have already. Several rhizomes of each variety could be placed in pots which are then stuck in the soil close together. In the spring just pull them out, soil and all, and place in holes in the newly prepped beds so as to reduce the trauma to the roots and maybe allow blooming next year.
I think it was Arlyn who last year cut several rhizomes into chunks, let them lay out of the ground all winter, then replanted the chunks in the spring. He had a better than 50% survival rate.
Keep us posted; we all like to learn more tricks.
