So last fall, I planted winter rye in the garden as a cover crop. I had read that it can be a pain to kill unless you let I grow until it has seed, but I figured it wouldn't be a big deal. Well.....I was wrong. I let it grow this spring until it was about 8" tall, and I've ve hoed this stuff under 3 times now, and I'm pretty sure I'll be picking it out all summer long. What. A. Pain.
On the other hand......it's done wonders for my soil. I've included a pic of what it looked like before, and a couple pics now. This is a one year old garden, started out with dead dirt that used to be the kids play place. It got 4" of compost tilled in, and the winter rye over the winter. It's now dark, crumbly, full of baby roots from the rye grass, and plenty of worms too.
I won't be planting it again this fall, I'll do something else, but I appreciate what it did for me this year.
Rye grass has a reputation as an awesome green manure. I didn't realize it was so "frisky."
A technique I have used to let fruit trees thrive in lawns is to sharpen a light shovel with a file and then use it to slice off the growing top layer of sod. I hold the back of the shovel nearly level with the sod and use it as a crude mandoline. The lower part of the turf survives but no longer monopolizes the space. This lets air and moisture reach the tree roots, whose feeders I can see. It seems to work. Maybe this would tame your ryegrass?
You have the option of pulling it up or waiting until the temps die it out.
I am not familiar with your locale so I am not sure when those temps will cause it to die.
Invasive plants are Earth's way of insisting we notice her medicines. Stephen Herrod Buhner
Everyone learns what works by learning what doesn't work. Stephen Herrod Buhner
Those are the largest trousers in the world! Especially when next to this ad: