Welcome to Permies, Benjamin!
What a great endeavor. I have a few links that might help you decide what to do. And experiences...
First, runner beans have never been perennial for me in zone 8a, so I'm thinking they won't in zone 7. There is a theory that you can dig the roots and replant them in spring - I haven't heard anyone pull it off, but maybe someone will pipe up. They are delicious and lovely plants, though. I just finished cooking the last fresh ones we harvested before the first hard frost. Mmm. We had them in a type of Mexican stew with tortillas.
In my experience though, the larger types of runner beans would completely overtake Jerusalem artichokes. I wouldn't put those two together, myself. When I grow full runners, they need a sturdy trellis. Also, it would be hard to harvest your runner beans if they were woven among a thick patch of sunchokes. Runner beans have a fairly tight window of tastiness, in my opinion. It would be easy to miss the majority if they weren't on a trellis.
Now you don't really need a perennial interplanted with a tuber crop, because you'll be digging the tuber. So maybe consider some annual options if you want to try a bean/sunchoke polyculture?
Here is a great thread linked below about the recent kickstarter and the penny vote that accompanied it. In the first post, main staple food crops are listed with the amount of calories they provide per acre. It might surprise you to find out that potatoes produce more than sunchokes!
In my experience with trying to develop a home-based diet, it's the most pleasant to grow the things that are
1. tastiest to you
2. easiest to store
3. grow very easily in your area. I leave sunchokes in the ground here because they have such short storage compared to potatoes. But that means loss to animals.
How many calories per/acre do common staple crops provide? Read here to find out!
https://permies.com/w/penny-vote
You also may want to check out one of my favorite threads.
Best Crops for a Survival Garden?
In that thread, people from all over post their zone, region, and their best survival crops. I posted my list for zone 8 in wet western Oregon, and then later posted my list for zone 8 in the dry, very hot and somewhat cold desert SW - and the two lists are quite different. That is such an educational thread. I love reading everyone's experiences.
And this is a fantastic video you might enjoy just for seeing the potential of even a small garden. It's very inspiring and has some answers that I've found helpful when people ask me things like "Is it really worth all your effort in growing food when you can just buy X at the market?"
Keep us posted with your progress!