Do you have fluorescent lights to grow the seedling under while they are indoors? Tomatoes, Peppers, and Beans are all warm weather lovers, so in MN you won't be able to plant them in the ground until towards the end of May, even with cloches. I don't put mine out until the first of June, and sometimes that is to early. Its way to early to start the bean seeds, they won't be happy in pots for more then 3 weeks or so. Most people direct seed them. Carrots are always direct seeded, as transplanting will stunt them.

Without fluorescent lights directly over (2") those plants will be very weak and spindly after two months of being indoors.

For hardening off, the direct sun factor is as/ or more important than the wind. The standard way to harden off plants is to bring them in and out, and in and out, lengthing the time they spend outside every day or so, obviously this will be a problem for you. Can you build a protective environment with screen to diffuse the light, and plastic to put over if it get cold, and keep them outside at your garden? I harden mine off by putting them on my screened in porch which only gets a few hours of direct sun, and is protected from the wind. I just put them out there and leave them - unless it is going to get down under 40 degrees - then I bring them in. I plant them in there beds on a cloudy day, or shade them for a day or two when they go into full sun.