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Digital envelope system: a modern take 
Envudu (envudu.com) looks very promising, and I think what they are planning to put out will do essentially everything you want. It's a single prepaid card, but with a connected app. On the app you choose which budget category you're going to spend on next, and then swipe your card. Your purchase gets deducted from that category. There aren't a ton of details yet on their website (e.g., what happens if you try to swipe on a category that doesn't have the funds available?) and there is going to be a $20/year fee, but I think it meets all of your criteria, even though it's a single card--you'll just need to use a smartphone with it.