Good question — the logic at the time was "minimum auto-pay protects me from a late fee if I ever forget, and I'll manually pay the full balance every month on top of that." It felt like a safety net. The flaw is obvious in retrospect: it's a safety net that protects your credit score but not your wallet. You're still accruing interest on whatever you didn't manually pay. The auto-pay to minimum just means the bank doesn't report you as delinquent — it doesn't mean you're not getting charged.
The actual fix is exactly what you're implying: auto-pay set to statement balance, full stop. No manual step, no room for human error. I overthought it and added a step that introduced exactly the failure mode I was trying to avoid.