I wonder if Country Gentleman would be more to your liking. It's a longer maturing variety than Truckers Delight/Truckers Favorite so perhaps that will give you much stronger stalks to grow the beans up.
Other than that you'll have to go with a field corn and harvest at the proper stage (milk stage) for your "sweet corn". Field corns usually excell at thick stalks, excessive roots systems (for anchoring) and height.
As for "spring peas", you should get more than two pickings, especially if sown broadcast style, which I highly recommend for your new ground.
You may also want to check your soil pH before adding your wood ash. It's easy to bring your soil pH up to neutral but if you overdose with ash it will be a much longer and more tedious process to bring it back from alkaline to neutral.
Shoe