What you described is almost exactly our situation, some 20 or 25 head of  brood cows, and we fed most all of the calves out.  Not enough hay, I had a round baler, and I followed the combine rolling up the pummies.  We put out 2 bales of clover hay, one bale of bean pummies.

Cows would always eat the bean pummies first, before touching the good clover.  as we got into the winter, we lost a couple of cows, and realized they just were not getting enough protein.  Started feeding mineral blocks, seemed to make a big difference.

We never did that again, too much risk.