Beginner Gardening: mystified and daunted by decades-old never-divided iris!, 1 by Carrie_N

Carrie_N wrote:
well, I don't know about NEVER, but I have inherited a patch that is perhaps forty years old, and hasn't been divided in probably 15? 20? years...more?? What I have looks more or less like three small car tires so tightly packed with roots and stems that they look like bales of straw. There are something in the neighborhood of a gazillion little pink buds within.

To make matters worse, I've never divided iris before! But I want to dive in and save this patch. But without killing them...would be so grateful for any guidance! I guess my main questions are:

* Is it too late in the season yet? I am in zone 5.
* A little experimenting shows that I can't really break anything up without prying the whole wad out of the ground. Am I endangering the whole patch by essentially replanting the whole thing? (see photo 1)
* Also found I can't separate anything, really, until I a) break off a big piece with the big shovel blade and then b) resort to a knife, sawing off bits. Are they as resilient as I hear, or am destroying them?? (see photo 2)
* Once I have a chunk that I am breaking smaller bits off (some will come by hand, others I saw, as I said above), I become filled with doubt, because while all have buds and a nice root ball, not many have the thumb-size rhizome/tuber I look for with my dahlias etc. I fear that those are all way below in the earth and I am fruitlessly ripping the plants off by their hair, and they will not come back...(see photo 3; chunk with tuber on the left, chunk with just root ball on the right).

thanks everyone!!!