RE: Turnips...
Bowman, Turnips prefer a soil PH of 6.5 -6.8, so if you could add some lime now that would be great. They will grow at a much lower PH, but to maximize the nutrients you already have in your soil, correct soil PH will help make those nutrients available.
If you could firm or pack the soil and then broadcast, and then use the atv to pack again, that would work well.
It does pay to keep an eye on the weather before planting and sow right before expected rain. However, the old-timers in my area always followed this rule "wet or dry, sow turnips on the 26 of July" They would do that regardless of the weather. IMO turnips should have at least 6 weeks before frost is expected. Of course that varies depending on the region.