For me, it is the mindless reptition or task accomplishment. Showers work well because I don't have to think about what I'm doing, which frees my mind up for something else. There's no rush, there's plenty of soothing ambiance, and it just works. I find doing chores around the house can trigger the same type of state. Putting dishes away lets my mind wander and problem solve. So does putting away laundry, dusting, sweeping, stuff like that. I usually need to wear earbuds and play an ambient noise to help me along.

But showers are still the best. You hit the nail on the head in your description about why it works. I think the key is anything relaxing, but not too relaxing such that you get drowsy.