@bluegrassmom
Hi Teresa, I've pondered this thread since you first posted. I don't deal with aggressive, hard-to-control grass, and I haven't tried wood shavings/sawdust, but I thought maybe I should go ahead and mention what I am trying with some of my iris.
I cut long lengths of cardboard (collected from the cardboard recycling bins around town), and I pinned them down between rows with garden staples. Then I covered the cardboard with wood chips. I kept the iris rows themselves uncovered and hand weeded whatever came up there. If I remember, I think I put a little fertilizer down before putting down the cardboard.
This definitely controlled the weeds between the rows. Some drawbacks: heavy rain would wash some wood chips around the iris plants. I would rake the chips away as needed while weeding the rows. I also noticed that iris roots were growing immediately under the cardboard.---Limited air exchange. Potentially could be some problems with this---maybe less vigorous plants or frozen roots in winter---but I couldn't tell that any iris were damaged.
I've only tried this a couple of times now for just a couple of years. The cardboard breaks down a fair amount by then. Probably this wouldn't work if you have hundreds of irises, but on a small scale it might be fine. As mentioned, the woodchips will tie up nitrogen as they decompose.
I'd be interested to hear any comments about this from everyone.