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I'm not an expert on the agriculture on the atlantic side, but I am fairly sure that everything in your list except for cabbage is possible.  My favorite cabbage substitute that grows anywhere is rape; it's more like broccoli leaves and doesn't make a ball like cabbage, actually it's more like collard greens which you can also grow if that's close enough to cabbage.  As with any garden, your best bet is to add abundant manure and/or compost and/or chemical fertilizer, and use local varieties that other people grow successfully, rather than buying seeds from far away.