Perennials as a rule need a cold/dormant time. No way in ND will they survive the winter in the boxes. You will have to bring them into a garage,and even then it could be too cold. I know my Dad still plugs his car in in the garage! I would not agree you are in zn 4. ND is zn 3 maybe even two up next to Canada. People like to plant LV's in boxes sunk in the ground so they do not take over. They can be very invasive. I am not sure what the best solution for you is. Let us know.

I'm in southern ND, closer to SD than to Canada by a longshot. Everything I've read and researched, including local farmers and nurseries say I'm zone 4.

I'm not worried about winter b/c I can bring them either into my heated garage which I keep at 45-50 in the winter or into the sunroom.

My biggest concern is whether they will get adequate sun/shade in that location. During the summer, on my porch, there's about 6-7 hours of sun and 7-8 hours of shade before it's dark. Is that going to be okay?

You are fine sun wise. Maybe too much sun. You will need to water water water.
Mine are in the shade, no direct sun light. I am now in central MN, and ZN 4 plants are iffy for me. LV's will do fine either zone. You may need to do some checking on your winter storage ideas. I know hosta need it below 40 for extended periods to go into dormancy. If they do not get their dormancy they die.

I spent a portion of yesterday thinning out my LV's. They like to wander and multiply. I thought of this post and am wondering why you want LV's in a planter? They will be sweet in a few weeks here, then they are just all leaves? Are you planting anything with them? You may get more resp. over in shade gardening. Woodland purists don't think much of LV's.