The cows have eaten it down so low I don't know if I even need to mow. That's what had me thinking I could maybe get away with it
Ya, you're fine, spray on a warm day & go heavy on the round-up. I might get scolded a bit on this but I might add just a little bit of 2,4-D. It'll help keep the grass seed from coming up this fall yet & if you go lighter, it'll be far gone by spring. Again, I'd go on the light end because it's a powerful herbicide & kills clover if sprayed on it but a little this fall would help long term on your plots for next year.