90 iris patches later...three days working on the iris clean-up and moss clean-up (not all, but many had moss). Put down lime and watered it in a bit. Hopefully it does the job. At least hope it helps. I'm guessing I will have to do this again since the moss was so bad. Some of the patches are in dug out holes (bad, bad for iris-I know). But year after year of digging out moss removes dirt too. I need to thin so many of them out anyway.
Thank you all for your advise. Here are a few before and after pictures.
Removing all that moss and then lime should help. When you have time, you may want to dig up the iris (after bloom time of course), add some soil to fill the holes, then replant the iris. If the moss is gone, then the raised iris may reward you.
"The chimera is a one time happenstance event where the plant has a senior moment and forgets what it is doing." - Paul Black
Here are a few before and after pictures. 
