Consider the possibility of Iris borers - a moth whose larva tunnel down iris leaves, feed on the roots (hollowing them out, mostly) and either spread or make iris roots vulnerable to bacterial rot.
I don't know if they occur as far north as you are (Nova Scotia?) but they are wide spread and occur in New England. I have had problems with them in the past, and the problems are recurring this year because I neglected to clean up the iris leaves when they browned and fell over in the late fall, or at least by late winter. The moths lay eggs in garden debris, including brown and drooping iris leaves, in late summer and fall. If you scrupulously remove dead iris leaves in late fall or very early spring (I have to do it both late fall and early spring in my mild climate)and keep other fallen or dead plant debris away from the irises, you can control them pretty easily. They make their way to the growing plant from the still attached dead leaves, or from fallen tree leaves or other dead plant debris lying up against the irises.
If you are finding not only mushy, rotted rhizomes, but are noting those not completely mush are hollowed out, the most likely culprit is iris borers. Cut away all hollowed or rotted rhizome, dust the roots with sulpher to treat the fungus spread by the borers, let them dry out just a bit in a shady place for a day or two and replant. Even a very small piece of rhizome with a little bit of root will regenerate, though it may take a couple of years before you have blooms again.
You may or may not see the catarpillers, but if you see little chewed corners on green iris leaves, or little holes or brown spots on the green leaves, with dark green, sappy-looking streaks running down the leaves, it is probably borers.
Once you have them, it is essential to clean up the iris beds very thoroughly every fall and/or early spring to avoid future problems.