In my (very limited) experience sunchokes grow too densely to let much else grow in between them. If you grow peas that don't grow past a meter you can sow them with oats or barley. I'm no expert, but my impression is that few "soup pea" varieties grow very tall?
As far as I know, the two traditional ways to grow drying peas here in Norway is with grains (for support, and to harvest some grain from the same field) or by themselves - the pea plants will cling to each other and form a big mat, which *may* lodge. I guess this depends on variety, soil and weather. With hand tools they could still be harvested, although more peas might be lost to mice, rot or sprouting if conditions were not good.
I've only grown peas with oats on a very small scale, but it worked well. I don't remember the proportions, but I think there was roughly 30-40 cm between the pea plants and 5-10 cm between the oats. They can be sown at the same time, grow at more or less the same rate, and are ready for harvest about the same time - presumably some varieties will work together better than others, but if you sow a mix and harvest and resow them together, suitable varieties and crosses will likely dominate after just a few generations. Especially if your field or bed is small enough to cull completely unsuitable ones before harvest, for instance those that do not compete well, set very few seeds, are susceptible to fungus, grow too well and pull down other plants etc.