On a TOU plan now, how are you actually shifting usage?

We're in a single-family home, and the evening peak rate is noticeably higher, and unfortunately that's also when our household uses the most power.

I've tried shifting laundry and dishwasher to off-peak, but the big stuff (cooking, AC, everyone home) can't really move. Starting to wonder if a battery is the only way to dodge peak rates.

For those on TOU, what actually moved the needle for you before (or instead of) buying storage?

Would especially appreciate examples from people in a similar type of home.