Roll with the cultipacker. If the WR is sprayed, it is just a matter of getting it on the ground so it decomposes. A cultipacker will do several things in addition to putting the WR on the ground. It will press seed into the ground. If you did min-till, it will remove any air pockets. It will put an un-even surface on the soil to reduce run-off and allow rain to soak in better. This is more important on clay soils or on slopes. If you have a slope cultipack across it rather than up/down it.
Sometimes I'll do both WR is easy to kill, but some weeds can be more problematic. Weeds are more susceptible to herbicides when they are young with new growth. So, sometimes, I'll mow about 2 or 3 weeks before broadcasting and spraying. This gives decomposition a head start but more importantly releases established weeds to produce new growth and some of the weeds seed released during mowing will have sprouted and be killed by the herbicide. I'll then broadcast, cultipack and then spray in the same day.
Thanks,
Jack