Generally irises are divided in July/Aug--pretty late for you and they may not settle in well.

if you have so many .. why not just get rid of some??? .. any you can do that anytime of the year ...

and leave some ... for doing it during the better time of year ...

just experiment .. its not like they are rare in your yard.. per your description ...

try sharpening your shovel .. this often helps slice thru stuff ...

ken

If you search dividing siberian iris in the perennials forum, you'll find many helpful posts. The search function is located at the top of the page.

I'm not sure that the OP has siberian irises. There is a species of iris called Blue Flag, and I have seen flag used to refer to bearded irises, so I ask the OP to come back to tell us exactly what he's got. Is it the native Iris versicolor or something else?

Yup you are correct - some sort of versicolour iris!

The only advice I found about dividing your blue flags said this:

4.) Divide blue flag iris rhizomes in the fall every 2-4 years when
they start to produce fewer flowers, or when your garden starts to
become too full of these plants. To start, cut the foliage back until it
is about half the size it used to be. Then, lift the rhizomes from the
soil with a garden fork. Cut the rhizomes with a sharp knife (dipped in
10 percent bleach solution to avoid plant disease) so that every section
has at least one eye. Remove the rotten and shriveled areas of the
rhizomes, as well as the older parts near the center of their rhizomes.

5.) After dividing, you can replant the healthy rhizomes in moist
organic soil slightly below the soil surface, with one end of the
rhizome sticking out.

(from https://lincolnlandscapinginc.com/blue-flag-iris/).

All the websites stress that the rhizomes are very poisonous, so definitely wear good gloves when you're dealing with these. As the advice says, a garden fork will make this much easier. Good luck!