So far as targeting smallmouth in the Bay, the earlier in June you go, the better. Depends on the year and water temps, etc. In warm years, I've seen them come off the beds in the Bay and disappear back out into the big lake by 6/1. In other, cooler years, they'll hang around a while longer. But mid-month is about the end of it even in cooler years.
The largemouth fishing should be about at its peak though. The weeds won't be so thick and high yet that they strangle the oxygen exchange in a lot of the smaller dents and coves in the Bay, including large sections of the Lagoons. This generally happens to a greater or lesser extent almost every year with the severity depending on water levels and how windy it has been.
Don't know the first thing about fishing for carp there, except that they are everywhere. On the other hand, if you want to be one of the nine or ten people in the state who have caught a gar on a fly rod, the weedy shallows behind the old Summerheim Pump Station on the extreme west end of the Bay used to be loaded with small gar.