Seems like a big waste of space to me. Take this with a grain of salt, first time ive done a garden in 35 years, but I'm an engineer and its all systems to me, lol.
Firstly, I beleive runner beans can be planted like 4 to 6 inches appart. Secondly, the only way they can attain energy from the gaps is if you give em something to grow on in the gaps. They arent self supporting. They are vines and like to grow striaght up as quickly as the support will allow... they seem to slow down after a while, so I think the beginning is important. They will start branching out, so 1 pole isnt great for all the arms of a single plant to grow up.
Below is a picture what i did. A single 10 gallon container (only half dirt), with maybe 10 to 15 bean plants... eight next to by cuc trellis. Inside the container, I mounted lots of bamboo to climb up, as well as the fence behing but they dont like it, they want to go UP, as many routes as they can to cover area. I used this to keep the 6 foot bamboo together, surprising it works fine indeed so long as bamboo is thick enough.
You can get the 6 ft bambo and connector on amazon, 8 ft bambo is better but double cost due to some shipping critical length.
For your situation, you need something much taller, and much more expansive... its okay, prefered imho, if the plants overlap and climb over each other.
So you could do what i did around each existing and train the side shoots to use it. Or you got get something MUCH taller to put in there straight up and down like you have now... but then youll probably want to grab some trellis netting and connect all the vertical into one giant wall of bean.
I.e. beans take much space... but they arent a bush so they can only use it if they have something to climb.