The decision
You've got the argument and the method. What's left is to decide, and I'd like the decision to fit in one sentence.
The card lives in a cupboard, not on me. I pay a fixed amount above the minimum on payday, dearest first, and I spend what's in the account.
Three parts.
The first is the freeze. Cards out of the wallet, frozen in the app, removed from every saved payment. The two lines on the fridge. A fortnight of living on the account before anything else changes.
The second is the order. A fixed amount you chose, by direct debit, on payday, to the dearest card. Minimums on the rest. The fixed amount moves, not shrinks, as each card clears. The end date on the sheet.
The third is the account. Spend what's in it. Cash for the evenings for a month. A small cushion once the dearest card is clear. No new credit while the sheet has a balance.
There's a form of planning that helps with rules like this, and it's been tested many times. Peter Gollwitzer and Paschal Sheeran reviewed ninety-four studies of it in 2006. You decide in advance what you'll do and when, in the form "when this happens, I'll do that", and people who plan that way follow through much more often than people who only hold the intention. So write three.
When I get paid, the fixed amount leaves for the dearest card that day, before I look at anything else.
When my hand goes to the wallet for the card and finds nothing, I'll check the account balance and decide from that.
When a card reaches zero, I'll move the fixed amount to the next dearest the same week, and put the cleared card back in the cupboard.
What to expect. This is my expectation and not a finding. The first fortnight will have a dozen reaches for a card that isn't there, and each one will be a small irritation followed by a decision, and the decisions will mostly be to buy the thing from the account and sometimes not to. The first month will end thin, and the thinness will frighten you a little, and the balance on the fridge will be lower than it was, which it hasn't been in years. Around the second month the fixed amount will start to feel like a bill rather than a sacrifice, because it goes out on its own and you've stopped noticing it. By the third month you'll know your month's shape without a gap in it, and you'll have stopped opening the card app, because there's nothing in it that changes. Somewhere between the sixth month and the end date on the sheet, the dearest card will reach zero, and you'll look at it, and the green number will say the whole limit, and it'll be the first time that number has been yours, and you'll leave the card in the cupboard anyway.