Are you really getting brassicas all the way to maturity in just 2 months? I plant as close to July 4 as the weather allows and I don't get maturity of beets, turnips, and radish until end of September at least. Interested to know what you're planting.
To answer your question about what to do from spring to brassicas planting, as with all things in MN it depends on the weather. IF I can get in the plots in May with a tractor, I plant oats. I know some folks from tropical, banana belt places like Iowa and Illinois will say plant clover as well, but IMO that's just a waste of good clover seed because you will be lucky to get 6 solid weeks of growth out of it before you must plant brassicas. Nitrogen fixation in that time is tiny. Oats are cheap, they cover crop well for weed reduction and they grow like crazy, plus as a disc-down green manure, they are beneficial.
However... More often than not, the weather does not cooperate and it's too wet to work dirt in early May. Once you get beyond the 15th of May there seems to me to be little point. Working up the plot, planting, etc, just doesn't leave enough time. I just spray the plot in mid-June to keep it fallow. Just no point in cover cropping if you only have 4 weeks of growing time or less, IMO. I start brassicas plot prep by spraying in late June, so if the spring is wet and slow, that just doesn't leave enough growing time to bother.