Berseem grows big n tall......
The brassicas might not be able to compete well. Oats should be ok.
Oats / rye I'd broadcast spread, then mow to about 3 or 4 inches. Brassicas I'd mow down some, then scratch a harrow with one pass, spread the brassica, then mow low. If it was me, I'd spray a quart of gly an acre on half the brassica spot instead of the 1st mow before the scratching. See which one does best. Definitely make sure you can pick up some oats or rye if it fails.
However, besides conservation mixes with berseem, trefoil, and perrenial rye, I have zero experince with annual clovers. I usually use red medium in new spots and grain mixes, ladino in shady areas, and white dutch if I want pure clover. Or mix those guys up.
Berseem might die all together with a gly spraying or low mow in a dry spell. Definitely do your homework.
Ive been dying to give crimson clover a try....... Just looks soooo nice. Not used much in NY though.