I forgot one important thing - the yield per square m in garden soil is very low, but I routinely plant other stuff in the same bed because it's pretty much incapable of strangling anything bigger than a seedling. Big seeds like climbing beans are much too vigorous to worry about, transplants of anything that can exceed 30cm are more likely to suppress the L.t than vice-versa.
You can dig the tubers any time between dying off and sprouting, but (unless it's a dry year) it's better at the early end; easier and they will have less damage - OTOH if you want to keep them you'll need some kind of clamp (spent compost or woodchip in a bin) or they will dry out - because they are rarely more than 3cm x 6cm - so never use any cooking method that could dehydrate them. Microwaving them whole in clingfilm is worth a try, and so is baking in well-sealed foil. It's worth leaving the skins on (they peel off easier when cooked), especially for boiling - otherwise all the flavour leaches out, and then they will taste like potatoes.
If I had broad hectares I'd probably grow mostly sweet chestnut - but the flowers are pretty, plus 'edible ornamental' and 'food security' are always good things.
Cheers.