You're worrying about less than nothing:
If you look at the
RR-1001 simulation results on P11 you'll see that 1" of ccSPF is sufficient for Chicago's climate with an asphalt shingle roof. At 1" a "brand-x" polyurethane foam is ~2-2.5 perms (and only ~ R6), so methinks you'd be good to go with ~1.3 perms (& ~ R15) in Milwaukee's only slightly colder climate. At 2" thickness ccSPF is ~1-1.25 perms, only slightly less vapor permeable than nominal for 3" of 2lb Icynene- close enough to be considered equivalent. Corbond is considerably less permeable than most SPF (0.6perms @ 1.5" thickness), but it's still the same order of magnitude.
With flash & batt walls you'll DEFINITELY need an interior side vapor retarder, but vapor-retardent latex and air-tight wallboard technique would be good enough.
But on both the walls & attic you'll do a lot better with wet-spray cellulose (even at standard density, not dense-pack) than any batt solution, and worth paying a premium over batts. Spray cellulose (but not dry blown) by itself will also qualify as the ignition barrier for the Icynene at 3" or more. With 3" of Icynene in the rafters the additional benefit of dense-packing the rest is small.
NO foam is a vapor
barrier (<<0.1 perms) and should be considered a vapor retarder. A 0.05perms poly sheeting at 0.006" passes substantially less water than a full cavity-fill of Corbond. Vapor barriers are two edged swords- too much of a good thing: They lock moisture out, but they also lock moisture in. Since most of the year the OUTDOOR temperature in Milwaukee is above the dew-point of conditioned space air, it's good to design structures that can dry in both directions when temperatures allow, but pass moisture slowly enough that you don't get seasonal accumulations of moisture in the structural wood that are high enough to create rot conditions. Closed cell foams are a useful tool, in that they do pass some water vapor, but slowly enough that it limits acute accumulation, but rapidly enough that the assembly dries. Anytime it's more than 37-40F outdoors in your location, the assembly can dry toward the exterior, which is most of the year in Milwaukee, but not much of the winter, which is why it's useful to have an interior-side vapor retarder to limit moisture flow as vapor during those winter months. A 1-2 perms takes many weeks to push much water through, in EITHER direction. A 0.1 perm it takes forever, and moisture can be trapped.