Just my opinion but I wouldn't disc, you will just be bringing tons of buried weed seed to the surface to germinate and grow. I have planted several plots into old pastures and hay fields in the last couple years with good luck, if it's not extremely tall I would spray it a couple times with...
If it were mine I wouldn’t touch it, just let the cereals die on their own and help feed and protect your clover from the summer heat and sun that is coming.
I totally agree and I am using the same equipment as you. I quit buying mixes years ago and started buying the seeds and making my own, bigger seeds in the big seed box and all the small seeds together in the legume box, no problems at all.